The Difficulties of Financial Inclusion via Large Banks:

Evidence from Mexico∗

Sara G. Castellanos† Diego Jiménez-Hernández‡ Aprajit Mahajan§ Enrique Seira¶

First draft: November 25, 2015This draft: March 27, 2019

Abstract

We provide evidence on why large financial institutions in developing economies have had difficultiesexpanding formal sector credit. Using detailed credit data and a product that accounted for 15% ofall first-time formal loans, we show that borrowers new to formal credit default at high rates andgenerate ex-ante unpredictable revenue. Using a large country-wide experiment, we show that ex-post contract terms do little to mitigate risk, implying moral hazard is not a primary cause of default.Failing to make its flagship financial inclusion product profitable, the bank eventually discontinuedit.

Keywords: Financial Inclusion, Credit cards, Default risk, Mexico.JEL: O16, G21, D14, D82.

∗We like to thank Bernardo Garcia Bulle and Isaac Meza for their outstanding research assistance. We thank StephanieBonds, Arun Chandrashekhar, Pascaline Dupas, Liran Einav, Marcel Fafchamps, Asim Khwaja, Melanie Morten, MauricioRomero, Carlos Serrano and Sirenia Vazquez for their helpful comments. We thank Ana Aguilar and Alan Elizondo for theirsupport. We also thank seminar participants at Banco de Mexico, the Central Bank of Armenia, Columbia, ITAM, The NavalPostgraduate School, Stanford, UC Berkeley, Yale, USC, UC Merced, BREAD (May 2018), UC Davis, Barcelona GSE Conference(June 2018), HKUST and UConn. All errors are our own. Previous versions of this paper was circulated under the titles“Financial Inclusion with Credit Cards in Mexico” and “The Perils of Bank Lending and Financial Inclusion: ExperimentalEvidence from Mexico.” The views expressed herein are those of the authors and do not necessarily reflect the views of Bancode México. AEA RCT Registry Identifying Number: AEARCTR–0003941.

†Banco de México, sara.castellanos@banxico.org.mx.‡Department of Economics, Stanford University, diego.j.jimenez.h@gmail.com.§Department of Agricultural & Resource Economics, UC Berkeley, aprajit@gmail.com.¶Centro de Investigación Económica, ITAM, enrique.seira@gmail.com.

1 Introduction

There is a growing body of work linking financial development to improved economic outcomesand some evidence that this relationship is causal.1 At the same time, a substantial fraction of theworld’s poor lack access to financial services, including formal credit.2 Yet, the barriers to increas-ing credit access through large financial institutions and the experiences of such institutions withlending to poor populations remain under-studied. While micro-finance lenders have receivedconsiderable attention, much less is known about the experiences of large banks whose scale, cap-ital and technology suggest they could play an important role in the universalization of financialaccess. For instance, there were approximately 2.3 million micro-finance clients in Mexico in 2009,while the single credit product we study, targeted at borrowers with non-existent or limited credithistories, taken alone had 1.3 million customers at the time.3 While many theoretical argumentshave been advanced to explain why large financial institutions find it difficult to lend to the poor(e.g. asymmetric information), there is little direct empirical evidence on the issue.

We use data from Mexico to detail some of the challenges faced by formal financial institutionsin lending to poor borrowers with limited credit histories (we will often use the abbreviation NTBborrowers to denote such new to banking borrowers). Broadly speaking, we ask whether largebanks, using traditional lending practices – individual liability, exclusive reliance on credit scoringand credit bureaus for borrower monitoring, and limited in-person interactions – can profitablylend to NTB borrowers. Combining a range of experimental interventions with detailed observa-tional data we conclude that the answer is likely in the negative. We focus on credit card debt –the most common formal borrowing instrument in the country – from a specific card (henceforththe study card) targeted at NTB borrowers issued by a large, successful commercial bank (BankA from now on). In 2010, the study card accounted for approximately 15% of all first-time formalsector loan products nationwide (Figure 1(b)).

We motivate our experimental results by establishing two facts about lending to NTB borrow-ers by large commercial banks. First, borrowers have high default rates – about 19% of our BankA sample defaulted on the study card over the 26 month study period. Newer borrowers are alsoriskier: default is twice as high for borrowers who had been with Bank A for less than a year rela-tive to borrowers who had been with the bank for more than two years (both measured at the startof the study period). We also document high default rates for NTB borrowers in a nation-wide

1For instance, Beck et al. (2007) show that about a third of the variation in poverty reduction rates across countriescan be explained by variation in levels of financial development. Burgess and Pande (2005) and Bruhn and Love (2014)provide evidence that this relationship is causal (for India and Mexico respectively).

2Banerjee and Duflo (2010) report that only 6% of the funds borrowed by the poor (in a survey across 13 countries)come from formal sources. The World Bank estimates that 60 percent of adults in developing countries do not use anyformal financial services and has called for Universal Financial Access by 2020 (see e.g. Demirgüç-Kunt and Klapper,2012; World Bank, 2017). In Mexico (the country that we study), a 2011 presidential decree established the NationalCouncil for Financial Inclusion to expand financial access to underserved populations. INEGI (2015) reports that by2015 only 57 percent all Mexican adults either had (43%) or have had (14%) an account at a financial institution and only43 percent either had (29%) or have had (14%) a formal sector loan of any kind.

3The estimate of the total number of micro-finance clients comes from Pedroza (2010) and the estimates for cardclients are from authors’ calculations using bank data.

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credit bureau sample, evidence that these default rates are a general feature of lending to NTBborrowers. Second, we use detailed customer level purchases and payments data to construct ameasure of bank revenue and show that it is low and variable for newer borrowers relative to olderborrowers and that revenue is difficult to predict even when using a large set of observables anda range of machine learning methods. We conclude that lending to NTB borrowers is risky andmuch of this risk is hard to predict at the time the card is issued. The role of ex-post (i.e. after thecard is issued) contract terms in mitigating risk then assumes even greater importance.

We then ask whether default can be reduced by altering two key elements of the credit cardcontract – interest rates and minimum payments.4 We estimate causal effects using a large-scalenation-wide randomized experiment carried out by Bank A, covering all 32 states (and 1360 out of2348 municipalities). The experiment randomly selected and allocated 162,000 pre-existing studycard borrowers to 8 treatment arms that varied annual interest rates (between 15%, 25%, 35% and45%) and monthly minimum payments (between 5% and 10%) for 26 months (from March 2007to May 2009). To our knowledge, this is the first paper examining experimental variation in boththe minimum payment and interest rate in credit card contracts. Furthermore, the magnitudeof experimental variation as well as the sample sizes are substantial. In addition, the samplingscheme ensures that the experimental results are representative of the bank’s national populationof study card customers (about 1.3 million at the start of the study).

We report five main experimental results. First, reducing the interest rate from 45% to 15%

reduces default by 2.6 percentage points (on a base rate of 19 percent) over the 26 month experi-ment. The implied elasticity is a relatively small +0.20.5 This is surprising. A positive correlationbetween default and interest rates (conditional on selection) is often interpreted as a measure ofmoral hazard. This correlation arises from both a debt or repayment burden effect (higher interestrates mechanically increase the debt burden) as well as a “pure” moral hazard or incentive effect(higher interest rates increase incentives for default independent of the debt burden effect). Thatthe combined effect is small implies that both effects are small. Second, taking advantage of thestratified experimental design we find that default elasticities are increasing in tenure with thebank so that interest rate changes are least effective for those borrowers for whom the asymmetricinformation problem is likely the most acute.

Some policy-makers, worried that low minimum payments could lead to excessive borrowingand increased default with negative consequences for both borrowers and the financial system,have advocated raising minimum payments.6 Higher minimum payments, however, could have

4Note that all borrowers had selected into the study card under the status quo contract terms that had a minimumpayment of 4% and an annual interest rate of approximately 55%.

5This contrasts with other work (e.g. Adams et al., 2009) who find that interest rates are an important determinantof default for U.S. auto loans. Our default responsiveness is considerably smaller than the effects on delinquency ratesdocumented in Karlan and Zinman (2017) although the authors do not report effects on default. It is also smaller thanthe elasticity implied by the Karlan and Zinman (2009) interest rate interventions in South Africa. See Table OA-22 fora comparison table.

6See e.g. Warren (2007); Bar-Gill (2003). In Mexico the Central Bank mandated a floor for minimum paymentsin 2010. In the United States policy makers have evaluated this possibility given that many minimum payments donot cover the finance charges (https://goo.gl/X8ujTi). Such prescriptions find some support in models of time-

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two opposing effects and it is not apriori clear which one will dominate. On the one hand, ceterisparibus, higher minimum payments reduce debt, easing the repayment burden, thereby reducingdefault. On the other hand, higher minimum payments tighten short run liquidity constraints,which increases default. The latter may be particularly relevant as, at the start of the experiment,73% of card holders’ monthly payments were less than 10 percent (of the amount due). Our thirdfinding is that doubling the minimum payment (from 5 to 10 percent of the amount due) had noeffect on default over the 26 month study period.7 This provides sobering evidence about theeffectiveness of limiting default through increased minimum payments.

We attempt to disentangle the two countervailing effect of the increased minimum paymentsby examining default in June 2012, three years after the experiment ended. After the experimentended, the second effect (tightened liquidity constraints) was no longer operational as all subjectswere returned to a common minimum payment (4%). However, debt is lower at the end of theexperiment in the higher minimum payment arms so the repayment burden is correspondinglylower. Our fourth finding is that the effect of the higher minimum payments on default was bothsubstantively and statistically significantly stronger in June 2012 than at the end of the experi-ment (May 2009). During the experiment the two countervailing effects cancelled each other out,highlighting the double-edged nature of increasing minimum payments as a policy tool to limitdefault.

The large variation in contract terms could also have affected borrower behavior with otherlenders. For instance, higher minimum payments could have led to borrowers substituting awaytowards other credit. We match our study sample to credit bureau data to answer this question.Our fifth finding is that the interventions had no effect on default across all other formal lenders. Inaddition, we find no evidence of crowd-out (or crowd-in) of borrowing, either along the extensiveor intensive margin, from other lenders. This is true both during the experiment and three yearsafter it ended.8 We argue that this lack of response is consistent with continuing credit constraints.

Finally, we explore possible reasons for the limited default response to the changes in contractterms. Default has significant negative consequences – we find that defaulting on the study cardis associated with a 80% reduction in the likelihood of a formal sector loan in the subsequent fouryears. Default then presumably forces borrowers towards informal credit. Using a nationally rep-resentative household survey we document that informal credit terms are significantly worse thanthe corresponding formal sector terms. Thus being shut out of formal credit and unattractive infor-mal sector terms may limit moral hazard responses to interest rate changes in our context. In lightof this argument, we then attempt to rationalize the high baseline default rates in our sample. Weconjecture that NTB borrowers may be vulnerable to frequent, large shocks that precipitate default,

inconsistent or unaware agents (Heidhues and Koszegi, 2010; Heidhues and Koszegi, 2016; DellaVigna and Malmendier,2004; Gabaix and Laibson, 2006). There is some evidence that time inconsistent preferences play a role in credit carddebt accumulation (Meier and Sprenger, 2010; Laibson et al., 2003; Shui and Ausubel, 2005) and that minimum paymentsserve as an anchoring device (Stewart, 2009).

7The point estimate is a statistically insignificant reduction of half a percentage point (the implied elasticity is +0.02).8Our results are then consistent with those documented in Karlan and Zinman (2017) and Angelucci et al. (2015) for

the microlender Compartamos Banco (in Mexico).

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though we are limited in our ability to test this convincingly. Using individual level social-security(IMSS) panel data linked to credit bureau data we estimate that unemployment is associated witha five percentage point increase in default a year later.

We draw two broad lessons from these results. First, it is difficult to expand credit to NTBborrowers via methods traditionally used by large financial organizations. Bank A stopped issuingthe study card entirely by 2010, providing some revealed preference evidence of the difficulty oflending to poorer clients.9 Second, ex-post contract terms do little to mitigate risk, suggestingmoral hazard is not a primary cause of default. We speculate that for our population other factors(e.g. employment shocks) may be more important drivers of default. This suggests a greateremphasis on insurance relative to credit in the expansion of financial access.

This paper connects with several strands in the literature on credit markets. First, a recentliterature identifies lack of access to formal financial services as a general problem in developingcountries and advocates supply-side interventions aimed at increasing financial inclusion – that isthe creation of broad-based access to financial services, particularly for poor and disadvantagedpopulations.10 We provide a detailed empirical analysis of the difficulties involved in expandingaccess to credit through large commercial banks as well as causal evidence on the effectivenessof standard policy tools to mitigate credit risk. Our work also adds to an earlier literature thatcritiques institutional, typically state-led and agricultural, lending to the poor.11 In this literature,limited formal private sector engagement with poor borrowers is taken as prima facie evidence ofthe inability of banks to do so profitably – our study provides detailed evidence on a private sectorbank’s attempt to lend to the poor, albeit in a different context.

We also contribute to the empirical literature documenting the existence and gravity of infor-mational problems in credit markets.12 We complement this literature (e.g. Karlan and Zinman,2009) by including borrowers who are new to formal credit – potentially important since asym-metric information problems are more severe for this sub-population. In addition, we examine therelative importance of liquidity constraints, repayment burden and “pure” moral hazard over along (five year) horizon. Relative to earlier work, the large, representative and stratified nature ofthe experiment allows us to examine responses for a range of borrowers with widely varying credit

9Other than microlenders, Banco Azteca (owned by Grupo Elektra, Latin America’s largest retail company) is oftencited as a success story in lending to under-served populations. Consistent with our findings of the limitations of tradi-tional lending technology Ruiz (2013) attributes its success to its ability “to leverage its relationship with a large retailchain (Elektra) to reduce transaction costs, acquire effective information and enforce loan repayment.” Banco Aztecaalso requires collateral, which invariably was in the form of household appliances (in case of default the appliance isusually resold by Elektra). In addition, the bank used screening techniques (such as home visits) and loan repaymenttechniques (weekly home visits from loan agents to delinquent clients) that are not generally used by large commercialbanks. Ruiz writes that the low default rate at Azteca could plausibly be related to its “crude collection and repossessionmechanisms.”

10This literature has largely been descriptive, documenting, for instance, the large numbers of people world-widewho do not use formal banking services. See e.g. Demirgüç-Kunt and Klapper (2012), though Dabla-Norris et al. (2015)is a notable exception. See also Dupas et al. (2018) who provide experimental evidence (from a multi-country trial) thata focus on expanding access to bank accounts by itself may only have limited welfare impacts.

11See e.g Adams et al. (1984). Aleem (1990) provides detailed estimates of the substantial screening and operationalcosts incurred by informal lenders in such environments. In our context, Bank A has relatively limited informationabout borrowers. See also Ruiz (2013) who examines the expansion of Banco Azteca in Mexico.

12See e.g. Ausubel (1991), Edelberg (2004), Karlan and Zinman (2009), Adams et al. (2009), Einav et al. (2012).

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histories. Finally, since we observe the totality of the experimental sample’s formal sector creditrecords, we can also measure spillovers and crowding out/in of other formal lenders in responseto the experiment.

The paper proceeds as follows: Section 2 outlines the various data sets we use and provides ba-sic summary statistics. Section 3 provides relevant institutional context and establishes four factsabout financial inclusion and credit in Mexico using a large representative sample of borrowersfrom the formal credit market and our sample from Bank A. Section 4 describes the experimentwhile Section 5 reports the effects of the experiment on default, cancellations and bank revenues,the primary outcomes of interest. Section 6 discusses some of the mechanisms driving the treat-ment effects documented in Section 5 and Section 8 concludes. Due to space constraints somerobustness analyses and secondary figures and tables are reported in the Online Appendices (OA).

2 Data, Study Card and Descriptive Statistics

We use six different data sets. First, we use a large representative sample of one million consumersfrom the Mexican Credit Bureau from 2010 that allows us to make population level statementsand comparisons. The second data set is a monthly individual level administrative panel for asample of 162,000 cardholders from Bank A. The third data set is also from the Credit Bureau andis an annual panel matched to the sample of 162,000 study card holders. The fourth data-set is theMexican Social Security data (IMSS) also matched to the bank and credit bureau data. The last twodata sets are nationally representative surveys (ENIGH, MxFLS). We next describe each in turn.

Credit Bureau Data (Representative Cross-Section): We use a random sample of one millionborrowers from the Mexican Credit Bureau (Buró de Crédito) both in 2010 and 2012 to describethe population of NTB borrowers in the country. A borrower appears in the credit bureau if shehas or has had a loan with a formal financial intermediary.13 For each borrower we observe thedate of loan initiation, the source and type of loan and her delinquency and default history.14 Wealso observe a limited set of demographics – age, gender, marital status and zip code. We use thisinformation to provide a snapshot of financial inclusion – in particular we describe the characteris-tics of first-time and recent borrowers, their sources of credit and their repayment history. We willrefer to this as the CB data.

Study Card: We use detailed data from a large commercial Mexican bank and a product (thestudy card) that accounted for 15% of first-time loans nation-wide in 2010. The study card isa credit card that can be used at a large set of supermarkets as well as other stores. Using the

13The Credit Bureau is required to maintain all records provided by reporting agencies for a fixed period of time. Asof September 2004 the Credit Bureau received information from 1,021 data suppliers including banks, credit unions,non-bank leasing companies, telecommunications companies, some MFIs, retailers (e.g. department stores), SOFOLES– limited purpose financial entities specializing in consumer credit, e.g. for auto loans and mortgages – and othercommercial firms (World Bank, 2005).

14We only have limited information on total loan amounts and no information on the interest rate and other contractterms. In addition, we do not observe credit scores.

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household level data from Atkin et al. (2018) from 2011, the study card could be used at storesthat accounted for 43% of all household expenditures at supermarkets and 16% of all householdexpenditures.15 The card was specifically targeted at low-income borrowers with no or limitedcredit histories.16 It had an initial credit limit of approximately 7,000 pesos, an annual interest rateof 55 basis points over the base rate and a monthly minimum payment of 4% of the total amountoutstanding. By 2009, Bank A had approximately 1.3 million clients with this card.

Bank Data (Experimental Sample): The sample consisted of a stratified random sample of studycard holders. Card holders were chosen subject to the additional constraint that they had paid atleast the minimum amount due in each of the six months prior to (and including) January 2007.This left the bank with a sampling frame of about one million clients from which the study samplewas drawn. The sampling frame was partitioned into nine strata based on tenure with the bankand payment behavior (each taking on three values), which the bank uses internally as predictorsof default (see Section 4.1 for more details). The bank then randomly selected a sample of 18,000clients per stratum. We use stratum weights (see Table OA-13) in all of our analysis to ensure ourresults are representative of the sampling frame. Within each stratum, clients were randomly as-signed to one of nine study arms so there are 2,000 clients per treatment arm within a stratum. Inwhat follows we will often restrict attention to the 8 primary study arms which gives us a totalsample of 144,000 clients across the 9 strata. As noted earlier, the resulting sample is geographi-cally widespread – covering all 31 states and the Federal District, 1,360 municipalities and 12,233zip codes. We examine the external validity of the sample for the national population of NTBborrowers below in Table 1.

The experimental data: Bank A ran a large country-wide experiment in an attempt to better under-stand and mitigate default on the study card, the bank’s flagship financial inclusion product. Theexperiment lasted from April 2007 to May 2009, and for this entire period we have monthly dataon purchases, payments, debt, credit limits and default. Default is defined as three consecutivemonthly payments that are less than the minimum payment. In these cases, the bank would re-voke the card automatically. Therefore we will refer to default and revocation interchangeably.In addition to this detailed transaction information we also observe some basic demographic vari-ables – age, gender, marital status and zip code of residence. Finally, we also observe default statusfor the study sample in June 2012, three years after the end of the experiment.

Matched Credit Bureau Data Panel: We were able to match the experimental sample to the creditbureau data once each year (from June 2007 to June 2010) and once more in June 2012. This enablesus to observe other formal sector transactions by the experimental sample thereby allowing us tomeasure effects on non-Bank A related outcomes (e.g. overall debt or overall default). We willrefer to this data as the matched CB data.

15We thank Marco Gonzalez-Navarro for kindly carrying out the calculations.16Internally the bank referred to them as the C, C- and D customer segments.

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Matched Social Security Data Panel: We were also able to merge our sample with the govern-ment’s social security agency’s records (IMSS) from November 2011 to May 2014 to obtain infor-mation on occupation and income for the 18% of the sample that worked in the formal sector andwas hence covered by the IMSS.

Survey Data (ENIGH, MxFLS): We also draw upon two national surveys to supplement the dataabove. We use Mexico’s income-expenditure survey (ENIGH 2004, 2012) to measure credit cardpenetration in the country and the Mexican Family Life Survey (2005 and 2008) to measure loanterms for both formal and informal loans.

2.1 Summary StatisticsThe experimental sample is of broad interest since the study card accounted for 15% of all first-

time formal sector loan products nation-wide. We provide summary statistics for this sample andcompare it to selected sub-samples from the CB data (columns 3-5). In Column 3 we use the CBsub-sample that had at at least one active credit card in June 2010, making it a nationally repre-sentative sample of the population of borrowers with at least one credit card (in 2010). Since ourexperimental sample is relatively new to formal credit, we next attempt to find a comparable groupin the CB data by constructing, albeit crudely, a sample whose credit history duration matches thatof the experimental sample. We do this by matching the distribution of the oldest credit entryacross the experimental and CB samples. This is the sub-sample for which summary statistics arereported in column 4 and we refer to it as the new (or recent) borrower sample.17 Finally, in Col-umn 5 we consider a sub-sample of experienced borrowers – those with a credit history of at least8 years (the median) in the CB data.

The experimental sample is just over half male, with an average age of approximately forty,about three-fifths of whom were married at the start of the study (Panel C). Other than marriagerates (which are lower in the CB) the figures are roughly comparable to those of the three CB datasub-samples. Borrowers in the experimental sample are somewhat less well-off relative to the av-erage CB member. For the borrowers that we could match to the IMSS, average monthly income (in2011) in the experimental sample is 13,855 pesos compared to an average of 14,759 for recent bor-rowers and 22,641 for experienced borrowers.18 Figure OA-7 shows that the distribution functionfor income for the experimental sample is first-order stochastically dominated by correspondingdistribution for the CB sub-sample from Column 3. Since we were unable to match 82% of the ex-perimental sample with the IMSS, we concluded that these individuals were in the informal sectorwith likely lower, less stable incomes.

Credit information also points towards our experimental sample being “marginal”. First, the

17The details of the matching procedure can be found in the Online Appendix Subsection A.1.18For comparison, average monthly per capita income in Mexico in 2007 was 4,984 pesos. The 25th and 75th per-

centiles of income for our experimental sample are 2,860 and 19,535 pesos respectively, while they are 2,580 and 6,000pesos for the country as a whole. Our income numbers are not adjusted for family size or for other earners in thecard-owner’s family. These numbers are conditional on working in the formal sector. We could match 18% of our ex-perimental sample and about 13% of the CB data to the IMSS. Well over half of Mexico’s labor force is in the informalsector so is not captured in the IMSS.

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mean credit score of 645 is low in absolute terms – borrowers with scores below 670 are typicallyineligible for standard credit card products.19 Second, the card issued by Bank A was the firstloan product for 47 percent of the sample. Third, our study sample was, unsurprisingly, at thelow-end of borrowing ability in the CB data. The credit limit for the study card was relativelylow at 7,879 pesos and the overall card limit for the experimental sample (across all cards) was15, 776 pesos in 2007, rising to 18, 475 pesos by June 2010. For comparison, in 2010 the meancard limit was 49, 604 pesos for the CB sub-sample with at least one active card, 22, 082 pesos forthe CB recent borrowers sub-sample and 56, 187 pesos for the experienced sub-sample. Fourth,borrowers have high rates of default; 17% of the experimental sample as a whole defaulted on thestudy card over the course of the experiment (the figure was 19% for the sample we will use as ourbase comparison group). Based on the figures presented above, we conclude that the experimentalsample was indeed drawn from a financially fragile population.

2.2 Bank Revenues per CardMeasures of bank revenues (and profits) from the study card are critical for understanding

the long term viability of financial inclusion through large commercial banks. We quantify bankrevenue from the study card using the detailed data on purchases, payments and debt over the 26month experiment (under assumptions explicated below).20 We define revenue for card i as

Revi = PV(Pay - Buy)i −Debt03/07,i + αiPV(Debt05/09,i) (1)

where PV(·) stands for the present value of the stream of payments inside parentheses that arediscounted at the TIIE (the Mexican inter-bank rate). If we observed a card from inception untilclosure, the exercise above would reduce to subtracting the net present value of payments from thenet present value of purchases. Unfortunately, we only observe cards for a 26 month window sohave to account for card usage before and after the experiment. We account for pre-study behaviorby subtracting the amount due from card i at the start of the experiment (March 2007). We assumethat post-study, borrowers make no further purchases and default on their outstanding debt withprobability φi in which case the bank recovers 10% of the amount due.21

Several features are worth noting. First, this measure of revenue accounts, albeit mechanically,for both default and cancellations. By the same reasoning it incorporates interest and fees.22 Sec-

19See Drenik et al. (2018). Unfortunately we cannot compare scores to the other CB sub-samples (Cols 3-5) since creditscores were not provided in these CB cross-sections.

20The exercise is analogous to the quantification performed in Adams et al. (2009) though the on-going borrowingon the card and data censoring (outside of the study period of 26 months) are important differences. Measuring bankprofits or revenues is relatively uncommon (Agarwal et al., 2015; Adams et al., 2009, are notable exceptions.) for lack ofdata.

21For each card i, φi is modeled as a function of its credit score using a non-parametric regression of default (duringthe 26 month window 03/07-05/09) against the credit score in June 2007 for the control group. We then assigned φi

based on the estimated regression evaluated at the credit score for i in June 2009 (see figure OA-11). The 10% figure fordebt collections is based on conversations with bank officials. The expected fraction (of the amount due) that would berecovered then is given by αi ≡ φi × 0.1 + (1− φi)× 1. Figure OA-12 in the OA shows that our measure of revenue isnot particularly sensitive to the choice of αi.

22In fact because of the identity Debtt = Debtt−1 +Buyt−Payt +(i/12)Debtt +Feest, an alternative representation

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ond, it is not a comprehensive measure of profit since it does not include promotion costs, thecost of the physical card and maintenance or administrative expenses or any income earned bymerchant discount fees or interchange fees. Nevertheless, in our estimation, it provides a usefulmeasure of bank revenue.

Figures 2(a) and (b) plot histograms of our revenue measure. The measure shows considerabledispersion — the standard deviation in panel (c) (7,347 pesos) is considerably larger than the mean(4,197 pesos) and newer borrowers exhibit even greater dispersion. To assess its reasonableness,we examine correlations with credit scores. Revenue displays an inverted-U pattern with respectto initial credit scores. Figures 2(c) presents a kernel regression of revenue on 2007 credit scores atthe borrower level for the control group, while 2(d) carries out the same exercise but for the stratumwith the shortest tenure with the bank. In private conversations, Bank A officials confirmed thataverage revenue, its dispersion, and its relation to credit scores are reasonable. Strikingly, clientswith low and high credit scores yield low revenues relative to clients with middling scores. Lowscore clients are more likely to default, thus yielding low revenue. On the other hand, high creditscore clients generate little revenue because they accrue lower interest charges and fees (e.g. bypaying off the amount outstanding each month). This inverted-U shaped relationship betweenbank revenues has been documented in other markets which gives us further confidence in ourconstruct.23

3 Financial Inclusion with Credit in Mexico

3.1 Traditional Banks Expand Credit to Underserved Populations

Formal credit penetration is low in Mexico,24 but has been growing, primarily by large banksusing credit cards to reach previously under-served populations. Figure 1(b) shows that more than70 percent of first time loans are through a credit card. The number of credit cards nationwidegrew from 10 million in the first quarter of 2004 to 24.6 million in the last quarter of 2011 witha substantial part of the growth being concentrated among lower income individuals (see Figure1(a)).25 Our study card played an important role in this growth (see Figure 1(c)).

This pursuit of low-income clients by large banks appears to have been, in part, inspired bythe success of Banco Compartamos and Banco Azteca.26 However, both Compartamos and Aztecapursue markedly different strategies than those used by Bank A. Compartamos uses joint liability

of equation (1) is∑T

t=1 (1 + r)−t [(i/12)Debtt + Feest]. We have information on late payment fees and overdraft fees,but do not directly observe merchant discount fees. The merchant discount fee is charged by the acquiring bank (i.e. themerchant’s bank) to the merchant and is 1.7% of purchases in our case.

23Fig. II.E in Agarwal et al. (2015) plots a inverted-U relationship using credit card data for the United States.24The ratio of private credit to GDP was 23 percent in 2010, while in the same year the figure was 52, 98, 43 and 40

percent for Brazil, Chile, Colombia, and Latin America and the Caribbean respectively. The percentage of adults with atleast one credit card was 17 percent (in 2014) compared to about 70% – 80% for the US. See US: https://goo.gl/bVWnaSand https://goo.gl/UG6pgn. For Mexico, see the “Reporte de Inclusion Financiera” (2016) (https://goo.gl/kYy4ae),Graph 1.12.

25See e.g. Banco de México (2016).26See e.g. https://goo.gl/7HufqG; https://goo.gl/vi2EYK; https://goo.gl/sjgoAn.

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(via group lending) while Azteca requires collateral (typically household durables). In addition,both lenders expend considerable resources on face-to-face interactions and home visits. This ap-proach is costly – both Compartamos and Azteca have higher operating expenses (relative to as-sets, see Fig OA-27) than Bank A – potentially limits the scale of inclusion and is quite foreign tolarge banks. An important question therefore is: can the lending model followed by large banks– non-collateralized credit, individual liability, limited debt collection efforts,27 credit bureau scor-ing, and limited in-person interactions – work in lending to NTB borrowers? In this section weprovide detailed evidence on why the answer may be no by highlighting some of the difficultiesfaced by Bank A’s study card operation.

3.2 Stylized Facts

We document four facts about traditional large banks’ experience of lending to NTB borrowers:(a) NTB borrowers default at high rates and default decreases with formal credit sector tenure, (b)revenue per borrower is low, variable, and (c) difficult to predict. Finally, we find suggestiveevidence for a first-lender externality, whereby better NTB borrowers are more likely to canceltheir cards, and quantify its impact on bank revenues.

A. High Default Rates

During the 26 month study approximately 19 percent of the control group defaulted on theircard (compared to an average cumulative 26-month default rate of 12 percent in the credit bureau).NTB borrowers for the study card are thus quite risky, even though the sample is presumablypositively selected since (a) it comprises successful applicants approved by Bank A using best-practice methods for large banks and (b) all borrowers had made at least the minimum paymentin the six months prior to January 2007.

Default risk, however, is not homogeneous. Figure 3(a) shows that newer borrowers are riskier:default rates for borrowers who had been with the bank for less than a year (the “6-11m” stratum)when the experiment began are 36 percent during the experiment, whereas the correspondingfigure for the oldest borrowers (those who had been with the bank for more than 2 years whenthe experiment began) are half that rate at 18 percent.28 The finding that newer borrowers areriskier also holds for a representative sample of NTB borrowrers in the credit bureau – mimickingthe experiment, Figure 3(b) examines all borrowers in the CB who had an active credit card as ofJanuary 2007, for whom this was the first card and who had not been delinquent in the previous6 months. We plot default in the next 26 months for this group (through May 2009) as a functionof card tenure. The study card has much higher default rates than other cards (even those withBank A) consistent with it being a “financial inclusion” product aimed at NTB borrowers. Bank Aoverall (across all cards) has default rates similar to those at other banks, suggesting our partner

27Mexican banks typically do not pursue default amounts less that 50,000 pesos.28These differing rates may be driven by at least three forces: positive selection, as riskier borrowers leave the market;

experience, as borrowers learn how to manage their cards; and lower moral hazard, as non-defaulting borrowers exertmore effort to avoid default to protect their reputation. We do not attempt to separate these.

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bank is at least as sophisticated as the others in the market. Finally, the negative slope shows that,across all banks, newer borrowers are more likely to default – for instance, borrowers with a cardtenure of less than 3 months are twice as risky as borrowers with a card tenure of 3 years.

B. Low and Highly Variable Revenue for Newer Borrowers

In spite of higher default rates, newer borrowers could in principle be more profitable (e.g.if they incur higher fees and/or take on more debt). This is not the case; Figure 3(a) shows thatrevenues were about 50 percent higher for older borrowers than for those in the newest borrowerstratum. In addition, the standard deviation of revenue is 7,198 for those in the 24+ months strata,and 8,738 in the 6-11 month strata. In other words, newer borrowers are a less attractive businessproposition than older borrowers.

C. Revenue is Difficult to Predict

Large banks’ lending procedures rely heavily on credit scoring and predictive modelling. Inother contexts such methods have led to significant credit expansions.29 It is unclear whether suchan approach is suitable for NTB borrowers who by definition have little or no credit informationto estimate such models. The performance of such methods with sparse information is ultimately,however, an empirical question.

We find that predicting revenue is extremely difficult in our NTB sample (see Table OA-9and Section B.3) using CB information available at the time of application and modern machine-learning predictive methods.30 We find an out-of-sample correlation (ρ) between predicted andrealized revenue of 0.04 for OLS models, and 0.28 for the best machine learning model (randomforests), while the root mean square error was 7,200 pesos (much higher than the 4,197 peso meanrevenue). Using CB information at the time the experiment began does not increase predictivepower, although adding information on ex-post behavior with the study card does increase theout-of-sample correlation to 0.41. Part of the difficulty in predicting revenue stems from the diffi-culty of predicting default (ρ=0.45) and voluntary cancellations by clients (ρ=0.15) and predictingwhich cards will pay interest (ρ=0.44).

D. The First Lender Externality

A new borrower’s repayment behavior on their first loan product generates valuable informa-tion about the borrower’s creditworthiness. To the extent that this information is public – via thecredit bureau – there is an externality since other potential lenders can now condition their lending

29See e.g. Einav et al. (2013).30We note that our sample consists of successful applications that are, presumably, positively selected for the out-

comes examined. The high prevalence of adverse outcomes (e.g default) even for such a population is indicative of themagnitude of the bank’s selection problem.

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on this information. Previous work has recognized the public good nature of this initial interac-tion in theory but there is little empirical evidence on its existence or magnitude.31 We providesome evidence for this externality and attempt to quantify its importance (within Bank A, thisphenomenon was widely recognized and referred to as “poaching”).

An implication of the externality argument is that new borrowers with larger improvementsin their credit scores should be more likely to obtain cards from other banks. We examine thispossibility in Figure 4 and find exactly this pattern. To focus attention on new borrowers werestrict our sample to borrowers for whom the study card was the first card and who had beenwith the bank for less than a year as of January 2007. These are precisely the set of clients forwhom the generated credit history should be most critical, as they did not have a credit score priorto obtaining the study card.

First, in Figure 4(a) we plot a non-parametric regression of voluntary client cancellation be-tween June 2008 and May 2009 against the change in credit scores in the preceding twelve months.Increases in credit scores are associated with higher borrower initiated cancellations. Virtuallynone of the borrowers that experience a decrease of 100 points in the credit score cancel, whereasmore than 8 percent of those that experience a 50 point increase cancel the study card. Second, inFigure 4(b) we plot non-parametric regressions of new card acquisitions between June 2008 andMay 2009 against the same regressor as in Figure 4(a). We see that increases in credit scores areassociated with increased card acquisition by NTB borrowers – 22% of borrowers with a 50 pointincrease in credit scores acquire at least one more card in the following year. The results supportthe idea that subsequent lenders use histories generated by the first lender to screen borrowers.32

A natural question then is how much revenue the first lender loses when a borrower is “poached.”To assess this we need a counterfactual – the earnings foregone by Bank A when a borrower ispoached. Note that a poached borrower need not cancel the study card but merely open anothercard with another lender. This will weakly reduce the first bank’s revenues (as long as the secondcard substitutes for the first for some purchases) and may also increase the likelihood of default.33

To simplify the calculation, however, we focus on borrowers who cancel their initial card whenthey leave Bank A for another lender (“switchers”).

We construct the counterfactual in a transparent way by matching switchers to non-switchers.In the interest of space, we relegate details to the notes in Table OA-11 which also displays thedifferent measures of revenue lost and placebos based on alternative assumptions. Our preferredestimates (Row 3, Column 1 in Table OA-11) suggest that the average revenue foregone by thebank for each switcher is 4,324 pesos, approximately the same as our revenue measure per card, a

31For instance, Stiglitz (1993) writes “The observation that another lender is willing to supply funds · · · confers anexternality, the benefit of which is not taken into account when the first lender undertakes his or her lending activity.”Petersen and Rajan (1995) conjecture that this problem is aggravated in more competitive markets, and indeed findthat newer firms (in the U.S.) in concentrated markets receive more financing than do similar firms in more competitivemarkets. In their survey piece, Banerjee and Duflo (2010) also note this problem and point out that the externality isparticularly acute in a pure adverse selection model.

32Interestingly, we note that good borrowers are also more likely to receive additional cards from Bank A itself (per-haps partly as a retention strategy).

33See e.g. Drenik et al. (2018).

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substantial revenue loss.34 This further attenuates the bank’s revenue gains from NTB borrowers,reducing its incentives to pursue financial inclusion.

4 Using Contract Terms to Change Behavior

The previous section documented high rates of card exit and variable revenues as well as the dif-ficulty of predicting these outcomes. This limited ability to screen borrowers ex-ante increases theimportance of ex-post measures such as contract term adjustments – the most important being theinterest rate on debt, the credit limit and the minimum payment required – in limiting default andmaximizing profits. For instance interest rate reductions may attenuate moral hazard. Similarly,minimum payment increases may limit indebtedness (as argued by policy makers) and subsequentdefault.

Whether and to what extent such variation in contract terms can mitigate default and its impli-cations for bank profits is an open empirical question. We were fortunate to observe a large-scaleexperiment conducted by Bank A that induced large experimental variation in interest rates andminimum payments (the bank did not experimentally vary credit limits).35,36 We use this experi-ment to transparently answer the question of the extent to which contract terms mitigate defaultfor NTB borrowers. In addition, we use our revenue measure to discuss the effects of the contractterm variations on bank revenue.

4.1 Experiment Description

4.1.1 Sample Selection

As outlined in Section 2, the sample frame consisted of all study card borrowers who had paidat least the minimum amount due in each of the six months prior to January 2007. The bankdivided this sample frame of more than one million study card clients into nine different stratabased on two pre-intervention characteristics which were used internally as default predictors: thelength of tenure with the bank, and repayment history over the past 12 months (both measured

34One may ask why Bank A – which presumably has more information about cancellers than other lenders – isunable to retain what appear (from the above calculation) to be highly profitable clients. Bank A could potentially limitdepartures by improving terms (e.g. lowering interest rates) for profitable potential switchers. There are, however,at least two limitations of such an approach. First, predicting cancellation may be a difficult exercise. Table OA-10in the appendix predicts voluntary cancellations using a battery of machine learning methods and finds AUCs in the0.6 – 0.7 range. This may help explain why researchers (see e.g. Ponce et al., 2017; Ioannidou and Ongena, 2010) havedocumented relatively limited price discrimination in credit cards and loans (in Mexico and Bolivia respectively). Giventhis, the bank faces a trade off between extracting rents from borrowers today at the risk of increasing the likelihoodof their subsequent departure (This trade off is modeled explicitly in (Taylor, 2003)). Second, after cancellation andobtaining a new card, it is not clear that the bank would wish to tempt the former client back since establishment of thesecond card could change Bank A’s profitability and risk calculations.

35We found out ex-post about the existence the experiment and were surprised by its size and by the magnitude ofthe changes in interest rates and minimum payments. The experiment was designed by the bank’s statisticians, and inconversations with bank officials it appears that the experiment was motivated by a discussion between Bank A and theCentral Bank about the causes of high card default rates.

36Aydin (2018) finds that experimental changes in credit limits have no effect on card default (at least over a ninemonth horizon).

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in January 2007).37 Each borrower was classified into one of three categories of tenure with thebank: (a) a long term customer who had been with the bank for more than 2 years, (b) a mediumterm customer who had been with the bank for more than one but less than two years, and (c) anew customer who had been with the bank for more than six months but less than a year. Eachborrower was also classified into one of three categories based on her repayment behavior over thepast 12 months: (a) a “full payer” who had paid her bill in full in each of the previous 12 monthsand hence accrued no debt, (b) a “partial payer” whose average payment over the past 12 monthswas greater than 1.5 times the average of the minimum payments required from her during thistime, and (c) a “poor payer” whose average payment over the past 12 months was less than 1.5times the average of the minimum payments required from her during this time. The product ofboth categories defined 9 strata, and 18,000 borrowers were randomly selected from each of thesestrata. We use sampling weights in our analysis to account for unequal stratum sizes and can thusmake valid statements about the entire sampling frame.

4.1.2 Experimental Design

Within each stratum, the bank randomly allocated 2,000 members each to each of 8 interventionarms and one control arm. Each treatment arm is a combination of two contract characteristics: (a)a required minimum monthly payment which is expressed as a fraction of amount outstanding(debt) on the card, and (b) the interest rate on the amount outstanding. The minimum paymentwas set at either 5% or 10%. The interest rate could take on one of four values: 15%, 25%, 35% or45%. The interest rate for the study card prior to the study was approximately about 55% so all theexperimental interest rates are reductions relative to the status quo. The two different minimumpayments and four different interest rates yield 8 unique contract terms. The experimental designthus identifies for each outcome and for each month 8 treatment effects within each of 9 differentstrata. In addition 2,000 customers within each stratum also served as a control group whosecontract terms did not change during the period of the experiment. The minimum payment forthe control arm was 4% but the interest rate varied across clients and, unfortunately, we do notobserve this rate in our data. Consequently, we do not use the control group as a contrast in mostof the analysis below and are explicit in the sequel about which arm serves as the reference orcomparison group. In most cases we use the 5% minimum payment and the 45% interest rategroup (abbreviated to (45, 5)) as the comparison group and we often refer to it as the base arm orbase group. Panel A of Table OA-14 in the Online Appendix tests the randomization procedureand shows that treatment assignment is uncorrelated with baseline observables.38

Figure OA-14 shows the time-line of the experiment as well as measurement dates. Each studyclient was sent a letter in March 2007 stating the new set of contract terms that would be in forcestarting in April 2007. Clients were not informed about the study or of any time-line for when thenew contract terms would change. The measurement of experimental outcomes began in March

37For borrowers with less than 12 months the full available history was used for stratification.38Panel B shows that the sample of non-attriters across treatment arms is also balanced along observables at the end

of the experiment.

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2007 and lasted until May 2009. During this period the interest rate and the minimum paymentwere kept fixed at their experimentally assigned levels. The experimental terms were not revealedto the risk department (in charge of deciding credit limits).39 The experiment ended in May 2009at which point all treatment arm participants received a letter setting out their new contract terms.These terms were the standard conditions with an interest rate of approximately 55% and a mini-mum payment of 4%.

We take advantage of the stratified randomization scheme to estimate simple regressions of theform:

Yi = β0 +7∑j=1

βjTji + δs + εi. (2)

where Yi the outcome of interest (default, cancellation or bank revenues) for borrower i and{Tji}7j=1 are a set of treatment indicators – the excluded group is the (45,5) treatment arm. Thestrata fixed effects, δs, are included in a way that allows us to interpret β0 as the base group mean.40

We use stratum weights (see Table OA-13) in all regressions.

5 Experimental Effects on Default, Cancellations and Revenues

We estimate the causal effects of interest rate and minimum payment variation on three primaryoutcomes – default, cancellations and revenue. Defaults are important for policy makers since theycan be a source of financial instability and may be particularly worrisome in poor populations. Infact, the experiment described in this paper was driven in part by the Mexican Central Bank’sconcern over default rates among NTB borrowers. Defaults are clearly important for banks aswell since they directly affect profits. In addition, the literature on credit market imperfections hasfocused on default in testing for moral hazard. We also examine cancellations – when the borrowerpays down her debt and cancels the study card. Comparing cancellations provides some evidenceon the effect of contract term changes on the relative attractiveness of the study card. Finally,revenues are our measure of the bank’s bottom line and the effect of contract term changes onrevenues is informative about the commercial feasibility of maintaining the altered contract terms.

5.1 Default

A. Interest Rate Changes Have Small Effects on Default

Default is a binary variable equal to one if borrower i defaults at some point during the 26month experiment and zero otherwise. Column (1) in Table 2 shows a substantial part (19%) of thebase group (i.e. the (45%, 5%) arm) defaulted over the course of the experiment. By comparison,the effects of the interventions were quite modest. Reducing the interest rate to a third of the base

39We cannot reject the null of no differences in credit limits across treatment arms at baseline and end-line (TableOA-15 and Figure OA-16).

40This is equivalent to estimating Eq. (2) with a full set of strata dummies and the additional constraint that∑

s δs = 0.Also, note that treatment assignment was done within each stratum and that the treatment assignment probabilities donot vary across strata.

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group rate (i.e. from 45% to 15%) reduced default by approximately two and a half percentagepoints over 26 months. The implied elasticity of default with respect to the interest rate is +0.20.This is considerably lower than the delinquency elasticity of 1.8 in Karlan and Zinman (2017) andalso lower than the default elasticity of 0.27 in Karlan and Zinman (2009) (see Table OA-22 for acomparison to other effects documented in the literature).

The treatment effects for the other intermediate treatment arms are also similarly small. The re-duction in default in the (25, 5) arm relative to the base arm is essentially the same as for the (15, 5)

arm (so that the corresponding elasticity is somewhat higher at +0.27) while the treatment effectfor the (35, 5) arm is estimated to be zero. The results for the comparisons between the (45, 10)

and the (r, 10) arms are even more stark with none of the estimated treatment effects being statis-tically different from zero (and the implied elasticities are all less than 0.1) – the higher paymentsattenuated the effect of the interest rate declines essentially to zero.

Interestingly, these effects are smaller for newer borrowers. For borrowers who had been withBank A for less than one year (as of January 2007) the elasticity is +0.08 while the correspondingelasticity for borrowers who had been with the bank for more than two years (as of January 2007)is +0.30, nearly four times as large. Thus, borrowers for whom the asymmetric information prob-lem is most acute are precisely those for whom the contract terms variations are least effective inlimiting default.

Figure 5 examines the evolution of default over the entire 26 month period by plotting theregression coefficients from estimating equation (2) month-by-month. The default measure at timet is a cumulative measure: i.e. Yit = 1 if i has defaulted at any point up to t. Default was essentiallyzero for six months, and we see only small declines in the last months of the intervention. Tosummarize, the consistent finding across all experimental contrasts and over all 26 months of theexperiment is that the interest rate decreases have negligible short-term and modest long-termnegative effects on default.

The large experimental variation in interest rates (from 45% to 15%) permits a clean test forthe presence of moral hazard, while the large sample sizes and stratified randomization ensurethat tests are well-powered for different sub-populations (e.g the most recent NTB borrowers).41

Moral hazard comprises a “pure” incentive or strategic (i.e. choice driven) effect and a repaymentburden effect, both of which should respond in the same direction to interest rate changes. Viewedin this light, the results above imply that both effects are small since their cumulative effect issmall.42 Since debt decreases over time, the flat time-path of initial default response (for the firstsix months) is consistent with the repayment burden effect being more important than the strategiceffect.

Thus, even though baseline default rates are high, it appears that moral hazard is not an impor-tant determinant of default at least for the range and nature of interest rate variations consideredhere. The treatment and strata variables together explain only about one tenth of one percent of

41Recall that all borrowers were pre-existing clients and had selected in under the same terms.42As Einav and Finkelstein (2011) note, however, the magnitude of the correlation test does not necessarily map

monotonically into the welfare loss from moral hazard. We do not attempt to quantify welfare losses here.

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the variance in default suggesting that default is driven in large part by forces not observed in ourdata (we examine this issue at greater length in Section 7).

B. Minimum Payment Increases Do Not Change Default

In contrast to the literature on interest rates and default, there is relatively limited empiricalwork on the relationship between minimum payments and default. However, minimum paymentshave received substantial attention in policy circles as a regulatory tool to protect consumers fromdefault driven by over-indebtedness.43 We view minimum payments as having two primary ef-fects: (a) a tightening of liquidity constraints and (b) a reduction in debt over the longer term.These will be a useful lens through which to interpret our findings.

The experiment doubled the minimum payment from 5% to 10%. This was a large and signif-icant change since 73% of borrowers paid less than 10% of the amount due before the experimentbegan (see figure OA-15). Table 2 shows that, perhaps surprisingly in the light of this figure, theminimum payment increase had no effect on default – the point estimate is a statistically insignif-icant increase of 0.5 percentage points on a base default rate of 19% for an elasticity of +0.02.44

The effects in the other arms are all broadly comparable, with the estimated elasticities rangingfrom −0.01 to +0.08. As with interest rates, the elasticities are smaller for newer borrowers (a sta-tistically insignificant +0.03) relative to older borrowers for whom the corresponding elasticity issubstantially larger (+0.10) and also statistically significant. This reinforces the point that it is pre-cisely those borrowers for whom the asymmetric information problem is most dire that are mostunresponsive to contract term changes. Next, examining the evolution of the treatment responsein Figure 5 we see that the minimum payment increase had minimal effects for the first six months,following which the default rate rose slightly and then stayed relatively stable thereafter.

The overall effects are small, particularly relative to the policy attention paid to increasingminimum payments as a means of limiting default. A key, albeit implicit, component of the policyargument is that increasing minimum payments should decrease debt which in turn should reducedefault. As we show in Appendix C.4.5, the first part of the argument is perhaps true – debt doesdecline, though it is imprecisely estimated (in part because of attrition via default and cancellation).However, any such reductions did not translate into lower default. In Section 6.1 we present some

43In Mexico, concerned over the size of minimum payments and its link to indebtedness and default (https://goo.gl/MkYbVO), the central bank mandated a floor for minimum payments in 2010. In the United States, a Congresscommissioned study found that minimum payment requirements had decreased markedly over time – declining from5% of outstanding balance in the mid-seventies to 2% by 2000 (Smale, 2005). In January 2003, US federal regulatorsissued inter-agency guidance on credit card lending that criticized minimum payments for being too low, noting thatsome did not even cover the finance charges and bills accrued in a billing cycle (https://goo.gl/X8ujTi). The CreditCard Act of 2009 mandated disclosures of how long it would take to pay off debt if clients only made the minimumpayment.

44The results are lower than those for delinquency in Keys and Wang (2016) but of the same order of magnitude asthose for default documented by d’Astous and Shore (2017). Both studies employ a quasi-experimental design to esti-mate causal effects using observational data from the United States. The latter document that an increase in minimumpayments of 2% on average over a base-rate of 3% increased default rates by 4% over two years (which implies anelasticity of .06). To our knowledge this is the first experimentally estimated effect of minimum payments on default.See Table OA-22 for a comparison table.

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evidence that the null effect is due to two countervailing forces (lower debt repayment burdenversus tighter liquidity constraints) off-setting each other.

Our results on the unresponsiveness of new borrower default are important for at least tworeasons. First, they show that the standard tools used by large banks have smaller effects on NTBborrower behavior than typically assumed in policy discussions. Second, the inability to con-trol default and cancellations affects the profitability of new borrowers, something we discuss atgreater length below.

5.2 Card Cancellations

Cancellation is a binary variable that equals one if borrower i voluntarily cancels her card atsome point during the 26 month experiment. Cancelling a card is an active decision which theclient can take after repaying the debt outstanding on the card. Cancellations are of direct interestbecause they provide evidence on the (change in) the study card’s attractiveness as a result ofcontract term changes and because they typically reduce bank revenues, thereby making financialinclusion harder.

A. Lower Interest Rates Reduce Cancellations

Table 2 shows that cancellations in the base arm (45, 5) were 13.4% over the 26 month period ofthe experiment, and that reducing the interest rate to 15% decreases cancellations by a statisticallysignificant 3.5 percentage points, for an implied elasticity of +0.39. The reduction in interest ratesmade the study card unambiguously more attractive and it is perhaps not surprising then thatfewer borrowers chose to cancel. This behavior is consistent with consumers engaging in somesearch or at least being open to outside options.45 Treatment effects from the other arms providebroadly comparable results. We next chart treatment effects using monthly data in Figure 5 whichpresents the regression coefficients from estimating equation (2) on a monthly basis. Cancellationsbegin to decline after about six months with the rate of decline remains roughly constant throughthe end of the experiment. To summarize – the results from all the experimental contrasts and overthe entire duration of the experiment show that the interest rate had a robust moderate effect oncard cancellations.46

That interest rate changes have larger effects on cancellations than on default is consistent withthe idea that non-preference factors play a larger role in the latter. The larger response also allowsus to rule out inattention as a cause for the limited effects on default. Finally, from the bank’s per-spective, the benefits from these decreased cancellations need to be compared against the revenuelosses from lowering interest rates, which we discuss below in Section 5.3.

45Section 3.2 presented evidence that cancellations are followed by account openings elsewhere for a selected sampleof “good” borrowers.

46It is, though, a bit unclear how to benchmark this finding. If we map cancellations to repeat borrowing for micro-finance borrowers, Karlan and Zinman (2017) find no effect of a interest rate reduction on the probability of repeatborrowing (p.18) by Compartamos borrowers over a 29 month period.

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B. Higher Minimum Payments Increase Cancellations

Doubling the minimum payment increased cancellations (over the entire experiment) by a sta-tistically significant 1.7 percentage points, for an implied elasticity of +0.12. The estimated treat-ment effects for the other arms are all roughly comparable with elasticities ranging from +0.12

to +0.24. As noted previously, the increase in minimum payments tightened short run liquidityconstraints which is consistent with increased cancellations.

Just as with interest rates, the minimum payment increase had a much larger effect on cancel-lations relative to default. One might reasonably have expected that this decline in attractivenessalso finds expression in higher default rates. That this is not the case suggests that default may beless strategic than cancellations.

5.3 Effects on Bank Revenues

Since we are concerned with studying financial inclusion via commercial institutions, revenuesare a critical benchmark for evaluating the effects of the intervention. In this section we examinethe effects of the interventions on revenue (we note that our measure of revenue is net-of-defaultin the sense that it incorporates default as detailed in Section 2.1). We find that departures from the(45, 5) arm reduced bank revenues. This is consistent with Bank A’s standard choice of minimumpayments and interest rates being profit maximizing (at least relative to the alternatives consideredin the experiment).

A. Lower Interest Rates Reduce Revenues

Table 2 shows that revenues are monotonically increasing in the interest rate. Taken literally,the point estimates imply that reducing interest rates from 45% to 15% over the 26 month period ofthe experiment reduced bank revenues (per borrower) by a substantial 2, 859 pesos (approximatelyhalf of the mean revenue measure) for an estimated elasticity of 1.54, with similar elasticities forthe other interest rate arms.

In the Appendix (sections C.4.4, C.4.6, and C.4.8) we explore the effects of the intervention onthree proximate determinants of revenues – purchases, payments and debt – and establish threefacts. First, interest rate declines have relatively small (although imprecisely estimated) effectson purchases – the Lee bounds for the elasticity are [−0.38,+0.25].47 Second, monthly paymentsdeclined modestly in response to the interest rate decreases (the Lee bounds are [+0.04,+0.39]).

Third, debt declined in response to the interest rate reductions and the Lee bounds are [+0.34,+0, 74].The small effects on behavior (purchases and payments) suggest that NTB borrowers had limitedsubstitution possibilities, and the fact that debt declined (and this decline was larger than impliedby the changes in payments and purchases) suggests that interest rate compounding is the domi-nant component of debt changes.

Extrapolating from the experiment suggests that increasing interest rates (relative to the ex-perimental choices) may be a profit maximizing strategy for the bank, even after accounting for

47We use Lee bounds Lee (2009), to account for the attrition caused by default and cancellation.

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default and cancellations – since our measure of bank revenue accounts for both. That the bank’sbusiness-as-usual interest rate was higher than 55% is consistent with this hypothesis.

B. Higher Minimum Payments Reduce Revenues

Perhaps more surprisingly, higher minimum payments also reduced bank revenues which are469 pesos lower in the (45, 10) arm compared to the (45, 5) arm, with an implied elasticity is −0.16

(the other contrasts are similar). In the appendix (C.4.7, C.4.9 and C.4.5) we find that the mini-mum payment increase led to modest increases in purchases and payments (the Lee bounds are[+0.18,+0.85] and [+.01,+.48] respectively). The point estimate on effect on debt shows a decreaseof about one-third though the the Lee bounds for the elasticity are quite wide – [−0.46,+0.15]. Thatlowering minimum payments increases revenue is also consistent with the bank’s standard mini-mum payment being 4% (lower than either of the experimental alternatives).

The revenue findings emphasizes the problems with using higher minimum payments as a pol-icy lever – higher minimum payments reduced bank revenues (lowering bank profits), increasedcancellations (thereby perhaps lowering borrower welfare) and had no effects on default duringthe experiment.

5.4 Spillovers and Long-Run Effects

We use the credit bureau data to examine whether the experimental changes in the study card’scontract terms affected borrowing with other formal lenders. For instance, lower interest ratesmight lead to increased cancellations of other – presumably more expensive – cards or clients mightchange their overall borrowing or default behavior on other loans. Similarly, higher minimumpayments might lead borrowers to look elsewhere for more attractive terms.

Table 3 shows that this is not the case. Neither default, cancellations nor new borrowing, (allmeasured in June 2009) with all other formal lenders respond to the changes in minimum pay-ments and interest rates. The results are unambiguous and demonstrate that even significant im-provements in credit terms, through lower interest rates, did not change borrowing patterns withother lenders. Next, although borrowers are more likely to cancel the study card in response tohigher minimum payments, there is no substitution towards other formal credit sources. We readthis as evidence for continued credit constraints in that borrowers in the higher minimum paymentarms while being more likely to cancel their cards were unable to replace the study card credit withother formal sector credit.

We were also able to obtain information from the credit bureau in June 2012, three years afterthe experiment ended. Columns 1 and 2 of Table 4 show the extensive margin treatment effectson other formal sector borrowing at that time. Consistent with the previous findings, we find thatbeing exposed to lower interest rates or higher minimum payments on the study card did not(at a five year horizon) lead to a greater number of loans or interactions with a larger number oflenders.48

48Karlan and Zinman (2017) also find no crowd-in or crowd-out among Compartamos borrowers.

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5.5 Bank A Discontinues the Study Card

In addition to the the limitations of ex-ante screening NTB borrowers documented in Section3.2, the previous results document that even substantial changes in contract terms were relativelyineffective at reducing default or increasing revenue (among pre-existing borrowers). Viewed inthis light, it is perhaps unsurprising that Bank A subsequently reduced its interactions with NTBborrowers. Figure 1(c) shows both the current stock and new issues of the study card over time.After issuing the study card in substantial numbers for several years, the bank stopped issuingit completely in 2009 and by 2013 there were no borrowers with the study card in the CB. Thus,financial inclusion using the traditional large bank lending model – even by one of Mexico’s mostsophisticated banks – turned out to be a fraught proposition.

6 What Explains The Limited Default Response?

In this section we explore possible reasons for the limited response of default to the experimentalchanges in contract terms. For the case of minimum payments, we argue that the null default effectarises from the “cancelling” out of two opposing forces and we identify the debt repayment burdenas a potentially important channel for explaining default. Second, we document that NTB borrow-ers are likely credit constrained with limited outside options, which might limit moral hazard anddefault.

6.1 Offsetting Effects of the Debt Burden and Liquidity Constraints

As mentioned earlier, increasing minimum payments sets in motion two counteracting forces.First, short-run liquidity constraints increase which could increase default. Second, over time in-creased minimum payments decrease the debt repayment burden, which should reduce default.The estimated null effect is consistent with these two opposing effects negating each other.

We can assess the reasonableness of this argument by studying default when one of the two ef-fects is no longer operational. We were able to obtain data on default for the experimental samplefor June 2012 (three years after the experiment ended). After May 2009, all study borrowers werereturned to the same set of contract terms. The minimum payment was set at the pre-experimentlevel of 4% and the interest rates were likewise returned to their pre-experiment levels (we confirmthis in Table 4, column (3) and in Figure OA-25). This means that for those previously in the 10%

minimum payment arms, the tightening of short-run liquidity constraints effect was no longer op-erational. On the other hand, since the higher minimum payments reduced debt (see C.4.5), clientsin the 10% minimum payment arm faced a lower debt repayment burden so the second effect wasstill present after the experiment ended.49 Thus, of the two countervailing forces described above,only the debt burden effect was operational after the experiment ended. The hypothesis is thenthat default should decline in the 10% minimum payment arms after the end of the experiment.

49For instance, the debt in the in the (45, 10) arm was lower than in the (45, 5) arm in May 2009 – although the Leebounds are wide and suggest reductions in the range of 760 pesos to no change in debt are both consistent with thedata. For the selected sample that survived through the experiment, debt reduced substantially, by about 30%.

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Table 4 shows that this is the case. Higher minimum payments (between April 2007 and May2009) decreased default through June 2012 by a statistically significant 4.6 percentage points. Theimplied elasticity of −0.11 is much larger and opposite in sign from the statistically insignificantelasticity of +0.02 at the end of the experiment in May 2009.50 The results are thus consistent withthe hypothesis that during the experiment tightened short-run liquidity constraints counteractedthe effect of a lower debt repayment burden yielding a zero net effect on default.

We can also directly examine the effect of the debt burden on default by using an instrumentalvariables strategy. The LATE of debt (measured in thousands of pesos in May 2009) on default(between June 2009 and June 2012) using the 10% minimum payment arm as an instrument is0.06, i.e. every 1000 peso reduction in debt due to increased minimum payments leads to a sixpercentage point reduction in default rates.51 Finally, the (Spearman) rank correlation between the7 ITT estimates of default and the reduction in debt in May 2009 across the 7 arms is 0.96 so that thatthe largest contrasts were those with the largest reductions in debt at the end of the experiment.

6.1.1 The Debt Burden Versus the “pure” Moral Hazard Effect

The previous section highlighted the importance of the debt repayment burden effect in deter-mining default using the minimum payment intervention. In this section we attempt to furtherquantify this effect by disentangling it from the “pure” moral hazard effect using the interest rateintervention.

We again use outcomes three years after the experiment to learn about the relative magnitudesof the two effects. During the experiment both effects should be operational. Since they bothincrease default and we found small default responses, we concluded that both effects were likelysmall. After the experiment, however, no differential “pure” moral hazard incentive effect wasoperational since borrowers across arms faced the same interest rates (see col. (3) of Table 4).However, Table OA-16 shows that the debt burden did vary systematically across the interest ratearms – the Lee bounds for the debt elasticity were [+0.34,+0.74], a robust effect.52 Consistentwith the debt burden hypothesis we find that default rates were lower in the lower interest ratearms three years after the experiment ended. Table 4 finds that five-year default rates in the (15, 5)

arm were 4 percentage points lower relative to the base arm – the implied elasticity is +0.15.53

50In the interest of clarity we focus on ITT estimates using cumulative default over the entire five year period fromMarch 2007 through June 2012. This has the advantage of avoiding the selection problems that would need to be dealtwith if we restricted attention to the non-attriters as of May 2009. On the other hand default now includes defaultboth during the experiment as well as after the experiment. We note, however, that at the end of the experiment (May2009) of the seven treatment arms, only two (the (15, 5) and the (25, 5)) arm had default rates that were substantively orstatistically different from zero. Four of the remaining arms had default rates that were (typically much) less than 1%away from the (45, 5) arm and none were statistically significant (see Table 2 for details).

51The exclusion restriction is violated if the 10% payment arm affected post-experiment borrower behavior throughchannels other than debt. For instance if two years of exposure to higher minimum payments changed borrower pur-chase and payment behavior, perhaps through habit formation. In Section Appendix D. we explore this hypothesis anddo not find much support for it. In addition, we only use those treatment arms with non-differential attrition in May2009.

52The Lee bounds are for the (15, 5) arm relative to the base arm.53This is approximately the same as the +0.20 elasticity at the end of the experiment which is estimated off a reduction

in default of 2.6 percentage points over the two year experiment. Note also that the 4% figure includes individuals whodefaulted during the experiment. We do not limit attention to post-experiment defaults only to avoid sample selection

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This finding further emphasizes the importance of the debt-burden effect in our sample of NTBborrowers.

This discussion needs to be qualified since the post-treatment effects may also be driven byother non-debt effects across treatment arms (e.g. borrowers in the lower interest rate arms maydefault less after the experiment if they expect favorable terms from the bank in the future). In theabsence of relevant data, we cannot rule out such non-debt channels. However, to the extent thatlower interest rates reduced default among more marginal borrowers (i.e. those who would havedefaulted absent the interest rate reduction), the post-experiment sample is likely not positivelyselected, which would mean higher (not lower) default in the lower interest rate arms after theinterest rate returns to 55%.

To conclude, the evidence on default particularly from the minimum payment arms suggeststhat the reduction in the debt repayment burden was an important channel for reducing defaultthree years after the end of the experiment.

6.2 Severe Consequences of Default May Limit Moral Hazard

Default has serious consequences for NTB borrowers, which may explain why default re-sponses were limited. Section 5 was indirectly informative about outside options. Recall thatdebt and interest rates are positively correlated, suggesting that clients had limited substitution al-ternatives. Here we provide evidence for three claims: first, NTB borrowers are credit constrainedin the formal sector and therefore presumably value formal sector credit. Second, default sharplyreduces access to subsequent formal sector credit. Third, informal credit terms are substantiallyworse than formal credit terms. These claims together suggest that the range of variation in con-tract terms, even though substantial, was “infra-marginal” in the light of these concerns and soborrower responses were limited.

A. NTB Borrowers are Credit Constrained

Using the methodology proposed in Gross and Souleles (2002), Section B.1 finds that our NTBsample is credit constrained: a credit limit increase of 100 pesos on the study card translates into 32pesos of subsequent additional debt. For comparison, this propensity to consume out of increasesin the credit limit is about thrice as large as the figure for the United States.

B. Default Reduces Access to Formal Credit

Default is associated with large declines in subsequent formal sector borrowing. Using theexperimental sample we estimate a cross-sectional regression where the primary explanatory vari-able is an indicator if borrower i defaulted on the study card in the six months after the start of theexperiment (i.e. between March and September 2007) and the dependent variable is an indicators

issues, but note that such concerns might in fact lead us to under-estimate the debt-burden hypothesis if it is the casethat the lowered interest rates led to more financially vulnerable borrowers surviving in the lower interest rate grouppost-experiment the (15, 5) arm had a 1.43% lower default rate than the base arm.

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for i obtaining a new loan or card six,twelve, or forty eight months after September 2007. We in-clude age, gender, and zip code indicators as controls, and restrict attention to the sub-sample forwhom the study card was the first formal sector loan product and who had been with the bankfor between 6 to 11 months at the start of the experiment. Panel A of Table 5 shows the results forall types of loans, while Panel B focuses only on credit cards. We further group columns by lendertype (any lender, all lenders except Bank A, and Bank A).

Default on the study card is associated with a substantial 26 percentage point decrease in thelikelihood of obtaining any new formal sector loans in the next 6 months (relative to a mean of29 percent for non-defaulters). The negative consequences of default are also long-lived – wecontinue to find substantial effects four years after default. Since default is reported to the CreditBureau, we might expect the negative correlation to show up not only in Bank A but in all banks,and indeed this is what columns (4)–(6) reveal. Panel B restricts attention to credit cards and finds,if anything, even starker results – default on the study card is associated with an absence of anysubsequent credit cards up to four years later. Lenders appear to adopt harsher stances towardsdefault on uncollateralized debt.

One concern with the regression above is that omitted variables may drive both default andfuture loan demand. We attempt to address this by adding borrower and time fixed effects. Thisincrease in flexibility forces us to restrict attention to delinquency as the primary outcome ratherthan default.54 We continue to find a negative relationship between delinquency and subsequentborrowing. The rate at which borrowers get loans from any bank is 7 percentage points per monthbefore being delinquent for the first time, but only 5 percentage points after the first delinquency.Borrowers cease to obtain any subsequent additional credit from Bank A following the first delin-quency.

We take the evidence above as being primarily suggestive, though the conclusion is unsur-prising.55 Decreased access to formal lending is precisely what one would expect from default ona formal loan given the Credit Bureau, though the magnitudes are striking. Defaulters are thenforced to rely on informal lenders and this is not an enticing prospect.

C. Informal Terms are Worse Than Formal Terms

We use the Mexican Family Life Survey (MxFLS) to compare interest rates, loan amounts, andloan duration for formal and informal loans.56 We find that informal loan terms are significantlyworse than formal loan terms. Table 6 shows the results from regressing contract terms on anindicator for a formal loan and controls. The first striking fact is that the average annual interest

54The problem with using default in an event study of this kind is that default is preceded formally by three eventsthat are reported to the credit bureau (three consecutive delinquencies over three billing cycles) so that the deteriorationin credit access precedes actual default. As a result we focus on the first delinquency for eventual defaulters.

55Bos et al. (2018); Dobbie et al. (2018) document similar magnitudes using more persuasive empirical designs.56We define a loan as formal if the lender is a bank and informal otherwise. Informal loan sources comprise: Co-

operatives (13%), money-lenders (8%), Relatives (38%), Acquaintances (20%), Work (11%), pawn-shops (5%), and others(5%). Consistent with the evidence from a range of developing countries (See e.g. Banerjee and Duflo (2010)) only 6%of borrowers have any formal loans and 91% of borrowers have only informal loans. Note that we do not observe anyinformal sector loans in our bank data.

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rate for informal loans is 291% while the corresponding rate for formal loans is 94 points lower(col. 1). The average loan amount is 3658 pesos for informal loans and 9842 pesos for formal ones(col. 4), and the term of the loan is 0.52 years for informal loans and 1.07 years for formal loans(col. 9). Figure OA-26 shows that the distribution of interest rates for informal loans stochasticallydominates the distribution for formal loan rates while the opposite is true for loan terms and loanamounts. These results are robust to controlling for income and wealth proxies (columns 2,4 and7). The results on loan terms and duration also survive the addition of household fixed effects.57

Based on these results we conclude that it is costly to be excluded from the formal loan market. Toconclude, default responded only in a muted fashion to even relatively large changes in contractterms perhaps because of the dire outside options outlined above.

7 What explains the high baseline default rates?

If default is indeed as costly as documented above, why are default rates so high? We speculatethat the answer is partly that NTB borrowers are vulnerable to shocks and such shocks precipitatedefault. The importance of the debt repayment burden documented above is consistent with thishypothesis.

We provide some evidence that shocks indeed precipitate default by estimating the effect oflosing a formal job on default. We observe employment spells for the the subset of our CB sampleemployed in the formal sector by matching the CB data with Mexican social security data (theIMSS). The matching yields a panel of 86, 363 individuals with information on employment historyin the formal sector as well as their formal credit records.58

We estimate the following regressions using OLS for individual i living in state s in month t:

defaultjit = αji + γjs,t +∑k≥1

βjk × 1( months unemployedit = k) + εjit (3)

where αi is an individual fixed effect and γs,t controls for trends at the state month level. Theindependent variables are a set of dummies 1( months unemployedit = k) that are equal to 1 ifindividual i in month t has been unemployed for k months. For individuals who are employed1( months unemployedit = k) is equal to zero for all k. The dependent variable, defaultjit is equalto one if individual i at month t has a ‘default code’ of j months, meaning that she has at leastone loan in delinquency for j or more months. Figure 6 plots βjk for different values of k andj. The likelihood of default is increasing in the length of the unemployment spell so that forinstance, being unemployed for 10 months is associated with a 5 percentage point higher likelihood

57Only about 3 percent of households hold both formal and informal sector loans so that the identifying variation inthe fixed effects model arises from a small (and likely selected sample).

58The matching proceeds as follows: Of the 1m borrowers in our 2014 CB data, 542, 959 had both a tax identifier aswell as a bank loan at some point between January 2011 and May 2014. We used the tax identifier to match borrowersto the IMSS monthly data from October 2011 to May 2014. We observe employment for at least one month for 86,363individuals. Since the IMSS is a census of all formal sector workers, a match indicates employment in the formalsector and we assume that a lack of a match indicates no employment in the formal sector. Since we do not observeemployment in the informal sector, we cannot construct a more comprehensive indicator of employment.

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of being delinquent on at least one loan – the unconditional mean is is 12 pp, so this is a 41%increase.59 These results demonstrate the severe effect of one particular shock (unemployment) ondefault (even after controlling for individual fixed effects). This is consistent with the view thatlarge negative shocks, such as prolonged unemployment (or health shocks), could increase defaultmarkedly. At the same time, these results are only partial since unemployment in the formal sectoris likely only one possible shock affecting NTB borrowers.60

8 Conclusion

Expanding financial access to under-served populations is a central part of the development agenda.While the role of innovative organizations and approaches, such as micro-finance, has receivedconsiderable attention, much less is known about the experiences of large financial institutionswhose scale suggests an important role in the expansion of financial access. In this paper we ex-amine a large Mexican bank’s efforts at expanding financial access with a credit card specificallytargeted towards borrowers with limited credit histories but that otherwise utilized standard largecommercial bank approaches to individual lending – exclusive reliance on credit scoring and creditbureaus for monitoring and limited client interactions. The card was available nationally startingin 2002 and by 2010 accounted for 15% of all first time formal sector loan products.

The bank’s experience was particularly difficult. We construct a measure of bank revenue perborrower and show that it is low, variable and unpredictable. In addition, the bank loses rev-enue as new borrowers with positive credit histories were more likely to leave the bank (for otherlenders). Moreover, newer borrowers defaulted at much higher rates that borrowers with longercredit histories. For these reasons, we conclude that ex-ante screening is likely a difficult task andthat ex-post contract terms assume even greater importance.

We find that adjusting contract terms ex-post does not reduce default. We use a large-scalerandomized experiment and show that even substantial changes in interest rates and minimumpayments have small effects on default. In the case of minimum payments, we show that the nulleffect may be explained by the offsetting effects of increased short-run liquidity constraints anda decreased debt repayment burden – highlighting the double-edged nature of higher minimumpayments as a policy tool for limiting default. The limited response to interest rate changes impliesa minor role for moral hazard even among our population of recent borrowers, and we providesome speculative evidence that other features of the economic environment (e.g. unemploymentshocks) may be more important barriers to financial inclusion. The difficulties of lending to thispopulation is captured most starkly in the bank’s abandonment of its flagship financial inclusionproduct and a declining engagement with borrowers with limited credit histories. Taken together,these findings highlight the difficulties of expanding credit access to under-served populations viafinancial organizations using traditional large-bank lending methods.

59The unconditional mean for the dependent variables are 18 pp. (>1m), 16 pp. (>2m), 15 pp. (>3m) and 12 pp. (>6m).60Only about 20% of our experimental sample is employed in the formal sector.

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Tables

Table 1: Summary statistics and baseline characteristics

Experimental Experimental Credit bureau sample

sample sample ≥ 1 Card Holders New borrowers Experienced(matched) borrowers

(1) (2) (3) (4) (5)

Panel A. Information from the experimental sample datasetMonth of measurement March 2007 May 2009

Payments 711 908 - - -(1,473) (1,811)

Purchases 338 786 - - -(1,023) (2,064)

Debt 1,198 5,940 - - -(3,521) (6,160)

Credit limit 7,879 12,376 - - -(6,117) (9,934)

Card revenue† 4,197 - - - -(7,347)

Credit score 645 - - - -(52)

(%) Consumers for whom experiment is their first card 57 - - - -(%) Consumers who default between Mar/07 - May/09 17 - - - -(%) Consumers who cancel between Mar/07 - May/09 10 - - - -

Panel B. Information from the credit bureau datasetMonth of measurement June 2007 June 2010 June 2010 June 2010 June 2010

Mean card limit (all cards) 15,776 18,475 49,604 22,082 56,187(15,776) (17,557) (32,596) (28,710) (43,032)

Total credit line (all loans) 53,652 64,804 53,718 49,348 139,804(70,292) (79,994) (103,503) (87,855) (162,568)

Tenure in months of oldest credit 68 100 79 68 206(54) (51) (87) (57) (85)

Panel C. Demographic informationMonth of measurement June 2007 June 2010 June 2010 June 2010 June 2010

(%) Male 52 - 47 47 53(%) Married 62 - 50 48 47Age (in years) 39 42 45 44 58

(6) (6) (19) (18) (22)Monthly income (10/11)‡ 13,855 - 14,391 14,759 22,641

(11,244) (12,949) (12,885) (15,928)Observations 164,000 - 221,151 57,450 55,120

Notes: This table presents means and standard deviations for selected variables from the experimental sample and three different creditbureau sub-samples. Column 1 shows statistics for the experimental sample at the beginning of the experiment – March 2007 (PanelA) and June 2007 (Panels B and C). Column 2 (Panel A) shows statistics for the experimental sample at the end of the experiment (May2009) and June 2010 (Panels B and C). Column 3 presents summary statistics for the credit bureau sub-sample restricted to borrowerswith at least one credit card in June 2010. Column 4 selects a sub-sample from the Column 3 sample that mimics the distributionof card tenure for the experimental sample (see the Appendix A.1 for details). Column 5 restricts the sample from Column 3 toindividuals with at least eight years of credit history with the bureau. (†) The card revenue measure is constructed using monthly dataon purchases, payments and debt and the procedure is described in Section 2.2. (‡) Income is obtained by matching our data withsocial security data (IMSS) from October 2011. The IMSS contains firm reports of employee earnings. Approximately 18% and 13% ofthe experimental sample and the CB sub-samples were matched with the IMSS.

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Table 2: Treatment Effects on Default, Cancellations, and Revenue(Outcomes measured in May 2009)

Default Cancellations Revenue

Strata: All 6-11M All 6-11M All 6-11M(1) (2) (3) (4) (5) (6)

r = 15, MP = 5 -0.026 -0.019 -0.035 -0.033 -2,859 -3,139(0.008) (0.002) (0.004) (0.007) (212) (353)

r = 15, MP = 10 -0.015 0.012 -0.011 -0.027 -2,642 -2,893(0.010) (0.004) (0.003) (0.003) (178) (314)

r = 25, MP = 5 -0.023 -0.014 -0.024 -0.026 -1,889 -1,956(0.007) (0.002) (0.004) (0.003) (140) (177)

r = 25, MP = 10 -0.008 -0.004 -0.003 -0.024 -1,893 -2,108(0.006) (0.002) (0.004) (0.005) (135) (294)

r = 35, MP = 5 -0.000 0.004 -0.018 -0.022 -964 -1,008(0.003) (0.002) (0.005) (0.005) (72) (132)

r = 35, MP = 10 -0.002 -0.010 -0.004 -0.003 -1,167 -1,062(0.006) (0.004) (0.002) (0.003) (114) (128)

r = 45, MP = 10 0.005 0.015 0.017 0.004 -469 -394(0.007) (0.005) (0.005) (0.003) (41) (118)

Constant (r = 45, MP = 5) 0.193 0.315 0.134 0.099 2,768 1,615(0.006) (0.001) (0.002) (0.004) (110) (189)

Observations 143,916 47,959 143,916 47,959 143,916 47,959R-squared 0.001 0.001 0.002 0.002 0.035 0.025

Notes: All regressions include strata dummies and use sample weights. The dependent variable for Columns (1) and (2) is default(bank-initiated revocations). The dependent variable for Columns (3) and (4) are (client-initiated) cancellations. The dependent vari-able for Column (5) and (6) is our measure of bank revenue from the study card. All outcomes measure the dependent variables at theend of the experiment (26 months). Columns (1), (3) and (5) include all cardholders in the experiment. Columns (2), and (4) and (6)restrict only the cardholders in the 6-11 months strata.

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Table 3: Treatment Effects on Other Loans: Default, Cancellations and New Loans(Existing loans by March 2007, Outcomes measured in June 2009, Any Loan Type)

Default Cancellations New loan

Any Same Other Any Same Other Any Same OtherBank Bank Bank Bank Bank Bank Bank Bank Bank

(1) (2) (3) (4) (5) (6) (7) (8) (9)

r = 15, MP = 5 0.006 -0.004 0.002 0.017 0.005 0.013 0.011 0.011 0.009(0.004) (0.002) (0.002) (0.007) (0.003) (0.005) (0.005) (0.005) (0.004)

r = 15, MP = 10 -0.006 -0.017 -0.001 0.016 0.006 0.011 0.018 0.009 0.011(0.003) (0.007) (0.003) (0.010) (0.003) (0.007) (0.011) (0.004) (0.007)

r = 25, MP = 5 -0.002 -0.014 0.003 0.005 0.002 0.003 0.009 0.003 0.003(0.002) (0.006) (0.003) (0.005) (0.003) (0.002) (0.007) (0.005) (0.005)

r = 25, MP = 10 -0.001 -0.008 0.002 0.003 0.006 -0.002 0.013 0.004 0.006(0.004) (0.007) (0.003) (0.006) (0.004) (0.004) (0.010) (0.004) (0.006)

r = 35, MP = 5 -0.002 -0.003 0.001 0.004 0.003 0.002 0.010 0.003 0.005(0.002) (0.004) (0.002) (0.002) (0.001) (0.002) (0.003) (0.001) (0.004)

r = 35, MP = 10 0.007 0.003 -0.001 0.006 0.002 0.005 -0.003 0.002 -0.007(0.002) (0.003) (0.006) (0.003) (0.003) (0.002) (0.002) (0.002) (0.002)

r = 45, MP = 10 -0.014 -0.010 -0.010 0.009 0.000 0.009 -0.004 -0.008 0.001(0.006) (0.006) (0.006) (0.005) (0.002) (0.004) (0.003) (0.003) (0.004)

Constant (r = 45, MP = 5) 0.560 0.336 0.449 0.137 0.021 0.121 0.541 0.165 0.490(0.002) (0.004) (0.002) (0.005) (0.002) (0.003) (0.004) (0.002) (0.003)

Observations 143,916 143,916 143,916 143,916 143,916 143,916 143,916 143,916 143,916R-squared 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Notes: All regressions include strata dummies and use sample weights. The regressions include all loan types (mortgage, auto loan,credit card, etc). The dependent variable for Columns (1) to (3) is default (bank-initiated revocations). The dependent variable forColumns (4) to (6) are (client-initiated) cancellations. The dependent variable for Columns (7) to (9) are new loan originations afterMarch 2007. All columns exclude the experimental card. Columns (1), (4) and (7) refer to loans issued by any bank. Columns (2), (5)and (8) refer to loans issued by the same bank as the experimental card (i.e. Bank A). Columns (3), (6) and (9) refer to loans issuedby any bank except for Bank A. All dependent variables restrict to loans that were issued on or before by March 2007 that remainedactive by March 2007. All outcomes are measured in June 2009, one month after the experiment ended.

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Table 4: Long-term Treatment Effects(Outcomes measured in June 2012)

New Loan # Banks Int Rate Cumulative Cumulative(any bank) active (Study Card) Default Cancellations

Jun 09 - Jun 12 Jun 12 Jun 12 Jun 12 Jun 12(1) (2) (3) (4) (5)

r = 15, MP = 5 0.003 0.012 0.002 -0.039 0.008(0.002) (0.006) (0.002) (0.013) (0.009)

r = 15, MP = 10 0.011 0.017 0.003 -0.066 0.027(0.006) (0.008) (0.001) (0.021) (0.013)

r = 25, MP = 5 -0.001 0.008 -0.001 -0.040 0.017(0.004) (0.008) (0.001) (0.011) (0.007)

r = 25, MP = 10 -0.006 0.008 0.001 -0.048 0.012(0.001) (0.004) (0.002) (0.014) (0.012)

r = 35, MP = 5 0.006 0.016 -0.003 -0.004 -0.005(0.005) (0.008) (0.003) (0.004) (0.002)

r = 35, MP = 10 0.015 0.002 0.005 -0.038 0.009(0.010) (0.004) (0.001) (0.007) (0.006)

r = 45, MP = 10 0.012 0.016 0.002 -0.043 0.021(0.005) (0.011) (0.002) (0.014) (0.007)

Constant (r = 45, MP = 5) 0.342 1.620 0.530 0.405 0.428(0.004) (0.005) (0.001) (0.010) (0.007)

Observations 139,197 139,197 42,463 139,197 139,197R-squared 0.000 0.000 0.001 0.002 0.000

Notes: All regressions include strata dummies and use sample weights. Each column is a separate regression. The dependent variablein column (1) is a binary variable equal to 1 if client i took out at least one loan between June 2009 and June 2012. The dependentvariable in column (2) is the number of banks with whom client i had an “active relationship” as of June 2012. An active relationshipmeans having at least one active loan with a lender. Column (3) uses as dependent variable the interest rate (between 0 and 1) on thestudy card in June 2012 for those cards that remained open. Columns (4) and (4) use as dependent variables binary variables that areequal to 1 if the client defaulted, or cancelled, respectively, at any point between March 2007 and June 2012.

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Table 5: Probability of getting a new loan or card against default

Any bank Any bank except Bank A Bank A

September 07 up to September 07 up to September 07 up toFeb/08 Aug/08 Aug/11 Feb/08 Aug/08 Aug/11 Feb/08 Aug/08 Aug/11

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Panel A. Any loanDefault in Mar/07 - Aug/07 -0.26 -0.33 -0.44 -0.21 -0.27 -0.37 -0.10 -0.15 -0.22

(0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.01) (0.02) (0.02)

mean dep. var non-defaulters 0.29 0.39 0.55 0.25 0.33 0.49 0.08 0.12 0.19(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Observations 22,813 22,813 22,813 22,813 22,813 22,813 22,813 22,813 22,813R-squared 0.363 0.366 0.370 0.363 0.361 0.369 0.346 0.359 0.365

Panel B. Credit cards onlyDefault in Mar/07 - Aug/07 -0.24 -0.31 -0.43 -0.18 -0.24 -0.34 -0.09 -0.14 -0.21

(0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.02) (0.02)

mean dep. var non-defaulters 0.23 0.30 0.42 0.19 0.25 0.35 0.07 0.11 0.18(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Observations 22,813 22,813 22,813 22,813 22,813 22,813 22,813 22,813 22,813R-squared 0.354 0.356 0.364 0.356 0.354 0.359 0.349 0.360 0.366

Notes: This table regresses measures of subsequent new card ownership against previous default on the study card. The sample con-sists of the set of borrowers with (a) the experimental card, that (b) belong to the 6-11 months strata, and (c) for whom the experimentalcard was their first formal loan. The observations are at the level of the card holder. Each column within each panel is a different re-gression. For all regressions the independent variable is equal to 1 if cardholder i defaulted in the experimental card between the startof the experimental period and 6 months after the experiment started (March 2007 to August 2007). The dependent variable variesby column. For columns (1), (2) and (3) in Panel A, the dependent variable is an indicator variable equal to 1 if a borrower obtains anew loan (any kind of loan: mortgage, auto loan, credit card, etc) in any bank between the periods September 2007 and February 2007,August 2008, and August 2011 (6, 12, and 48 months). Columns (4), (5) and (6) repeat the exercise but restricting to loans with banksthat are not Bank A, whereas Columns (7), (8) and (9) restrict to Bank A, exclusively. All regressions include postal code fixed effects,age, a male dummy, and a married dummy. Standard errors are shown in parentheses.

Table 6: Formal vs Informal Loan Terms

Interest rate Loan amount Loan duration in years

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Formal credit -94 -108 -7.08 6,184.3 4,926 3,934 0.554 0.544 0.491(31) (48) (38) (288) (484.3) (659.3) (0.034) (0.058) (0.104)

Education dummies No Yes No No Yes No No Yes NoSample dummies Yes Yes Yes Yes Yes Yes Yes Yes YesHousehold controls No Yes No No Yes No No Yes NoHousehold FE No No Yes No No Yes No No Yes

Dependent variable mean 254 254 231 5022 5022 5061 0.732 0.732 0.732Dependent variable SD 503 503 423 6,938 6,938 7,023 0.757 0.757 0.757Observations 2,427 880 202 8,810 2,992 423 4,257 1,522 301R-squared 0.006 0.036 0.860 0.063 0.171 0.661 0.083 0.119 0.646

Notes: Data from National Survey of Household Living Standards (Rubalcava and Teruel, 2006) is used to construct the table. Thetable shows the difference between formal and informal interest rates (Columns (1)–(3)), peso loan amounts (Columns (4)–(6)) and theloan duration (Columns (7)–(9)). We consider a loan to be from a formal entity which we define as a banking institution and informalotherwise. The household controls include age, monthly expenditures, and dummy variables for car ownership, washing machines,and other household appliances. Standard errors are shown in parentheses.

31

Figures

Figure 1: Credit Card Growth, Study Card and First Time Loans and Study Card Stocks and Flows

0.2

.4.6

Frac

tion

of h

ouse

hold

s (2

004)

050

100

150

200

Gro

wth

in C

C h

oldi

ngs

(%, 2

004-

2010

)

1 2 3 4 5 6 7 8 9 10Income decile

Growth Fraction of households

(a) CC Growth and share of HH with CC’s0

.25

.5.7

5Fr

actio

n of

indi

vidu

als

Credit cardPersonal loan Credit line Real estate Auto Other

Experimental type of cards

(b) First Time Loan, by type

0.5

11.

52

ratio

of c

ards

with

resp

ect t

o Ja

n/06

Jan/06 Jul/07 Jan/09 Jul/10

total number of cards issued cards

(c) Study Card Stocks and Flows

Notes: Panel (a) is constructed using data from the 2004 National Income Expenditure Survey (ENIGH). The X-axis represents (house-hold) income deciles. The left Y-axis – corresponding to the hollow bars– shows the percentage growth in the number of householdsthat have at least one credit card from 2004 to 2010. The right Y-axis – associated with the red line – plots the fraction of householdsin each income decile that have at least one card in 2004. Panel (b) is constructed using a representative sample of the 2010 creditbureau population (i.e those with formal sector loans). For each individual, we identify the oldest loan and record its type (e.g. autoloans, credit card, real estate loans). We then plot the fraction of first loans by type. The gray area represents the study card describedin Section 2. Panel (c) is constructed using credit bureau data from 2012 on Card A. For confidentiality purposes we normalize theJanuary 2006 values for both the total number of study cards and the number of issued study cards to 1. The solid blue line representsthe total number of study cards in a given month. The red dashed line represents the flow of study cards: the total number of newstudy cards were issued in a given month.

32

Figure 2: Distribution of Measured of Revenue per Card and relation to Credit Score

0.0

2.0

4.0

6.0

8.1

Frac

tion

of c

ardh

olde

rs

-20 -10 0 10 20NPV of Revenue (MXN thousand pesos)

(a) Net Present Value of Revenue (’000 Pesos)(control group borrowers)

0.0

2.0

4.0

6.0

8Fr

actio

n of

car

dhol

ders

-20 -10 0 10 20NPV of Revenue (MXN thousand pesos)

(b) Net Present Value of Revenue (’000 Pesos)(control group borrowers with 6-11M)

25th

per

cent

ile

50th

per

cent

ile

75th

per

cent

ile

-4-2

02

4N

PV

of R

even

ue (M

XN

thou

sand

pes

os)

525 575 625 675 725Credit Score in June 07

95% CI lpoly smooth

kernel = epanechnikov, degree = 2, bandwidth = 31.84, pwidth = 47.76

(c) Mean revenue by Credit Score(control group borrowers)

25th

per

cent

ile

50th

per

cent

ile

75th

per

cent

ile

-4-2

02

4N

PV

of R

even

ue (M

XN

thou

sand

pes

os)

525 575 625 675 725Credit Score in June 07

95% CI lpoly smooth

kernel = epanechnikov, degree = 2, bandwidth = 48.37, pwidth = 72.55

(d) Mean revenue by Credit Score(control group borrowers with 6-11M)

Notes: Panel (a) represents the distribution of our revenue measure for the control group (using sampling weights). Panel (b) rep-resents the analogous graph for the new to banking strata. For clarity, the histograms are censored at ±20, 000 2007 Pesos. Panel (c)displays a local polynomial kernel regression of our revenue measure against credit scores in June 2007 done at the individual cardlevel (for the control group). The grey shaded area denotes point-wise 95% confidence intervals. The x-axis ranges from 5th to the95th percentiles of the credit score distribution. Panel (d) presents the analogous graph for the new to banking strata.

33

Figure 3: Default and revenue by months with the credit card

010

0020

0030

0040

00N

PV

of r

even

ue (M

XN

pes

os)

0.1

.2.3

Pro

porti

on o

f car

ds w

ho d

efau

lt

6 - 11 12 - 23 24+ Months with credit card

default revenue

(a) Default and revenue by months with the credit card

0.1

.2.3

.4P

ropo

rtion

who

def

ault

by M

ay/0

9

1 6 11 16 21 26 31 36Months since card was opened (Jan/07)

study card bank A w/o study card all banks

(b) Tenure at CB and future default, CB sample

Notes: Panel (a) plots default (in dark blue) and revenue (in light red) during the experiment on the study card for three differentstrata defined by the length of time the borrower had had the study card prior to the start of the experiment (tenure). We restrict tocardholders from the control group of the experimental sample. The blue bars represent the proportion of cardholders who defaultedat any point in time between the beginning and end of the experimental period (March 2007 to May 2009). The red bars represent themean NPV of revenue by card from March 2007 to May 2009. We use stratum weights and the error bars show the confidence intervalfor the estimate of the mean. Panel (b) uses the control group of the experimental sample and the 1 million representative sample fromthe Credit Bureau. The red diamonds show, for the control group, the proportion of cardholders that default by the months since thecard was opened (binned into quarters because of the sample size). The blue squares and green circles repeat the sampling exercisein the credit bureau data. The green circles use all cards, whereas the blue squares restrict attention to Bank A cards that are not thesame type as the study card (identified by the first 6 digits of the card). To mimic the sampling frame from the experimental sample,we restrict attention to credit cards that were opened on or before Jan 2007 that had been non-delinquent in the last 6 months prior toJan 2007. For each of these cards, we plot the probability that the card is on default on before May 2009 (y-axis) against card tenure asof January 2007 (x-axis). The resulting graph shows that newer borrower in the formal credit market are more likely to default.

34

Figure 4: Client “Poaching” and the First Lender Externality

0.0

2.0

4.0

6.0

8

Pro

porti

on o

f clo

sed

acco

unts

from

Jun

e 20

08 to

May

200

9

-100 -50 0 50Change in credit score from June 2007 to June 2008

Cancelled by Client

(a) Card Closings and Changes in Credit Scores

0.0

5.1

.15

.2.2

5

Pro

porti

on th

at g

et lo

anfro

m J

une

2008

to M

ay 2

009

-100 -50 0 50Change in credit score from June 2007 to June 2008

With any other bank With the same bank

(b) New Loans and Changes in Credit Scores

Notes: These figures use data from borrowers in the experiment who had been with the bank between six and eleven months (as ofJanuary 2007) and for whom the study card was the first card of any kind (24,146 individuals satisfy these criteria). Panel (a) showsa local polynomial kernel regression where the explanatory variable is the change in the credit score from June 2007 to June 2008.The dependent variable is an indicator for whether a borrower cancelled the study card between June 2008 and May 2009. Panel (b)shows two local polynomial kernel regressions where the explanatory variable in each case is the same as in panel (a). The dependentvariables are binary variables for whether a borrower obtained a new card (between June 2008 and May 2009) either from Bank A (reddotted line) or from any other bank (blue line with triangles). Dashed lines represent point-wise 95% confidence intervals.

35

Figure 5: Default/Revocation and Client Initiated Cancellations

-0.04

-0.02

0.00

0.02

0.04

Trea

tmen

t Effe

ct (p

rop)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: interest rateDependent variable: cumulative cancellations

-0.04

-0.02

0.00

0.02

0.04

Trea

tmen

t Effe

ct (p

rop)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: minimum paymentDependent variable: cumulative cancellations

-0.04

-0.02

0.00

0.02

Trea

tmen

t Effe

ct (p

rop)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: interest rateDependent variable: cumulative default

-0.04

-0.02

0.00

0.02

Trea

tmen

t Effe

ct (p

rop)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: minimum paymentDependent variable: cumulative default

Notes: Figures plot monthly treatment effects. For each month we regress the outcome (default or cancellation) on all treatmentand stratum indicators using sampling weights. For clarity, we only display treatment effects for a subset of treatments. Each dotcorresponds to the coefficient on the treatment indicator for that month along with the point-wise 95% confidence interval. Thatis, each point represents the difference between the means of the plotted treatment and comparison group. In all sub-figures, thecomparison group is the (45%, 5%) group. For the graphs on the left – examining the interest rate changes and colored red– thetreatment group is the (15%, 5%) arm. For the graphs on the right – examining the minimum payment treatment and colored blue– the treatment group is the the (45%, 10%) arm. In all sub-figures the dependent variable is either (a) cumulative cancellations (toprow) or (b) cumulative default (bottom row).

Figure 6: The “Effect” of Unemployment Spells on Delinquency

-.05

0.0

5.1

incr

ease

in p

roba

bilit

y (β

)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Months since last employed

dep. var >1m >2m >3m >6m

Notes: The figure presents βjk estimates from (3) estimated using OLS. The data is matched CB-IMSS data at the borrower-month level.

We observe employment for 86,363 borrowers from 10/11 to 05/14 (unbalanced panel). Each line corresponds to a regression with adifferent measure of delinquency – delinquency is defined as j-months past due where j ∈ {1, 2, 3, 6}. The β coefficients are intendedto capture the associational effect of unemployment spells (by duration of unemployment) on delinquency . For instance β3

6 is thecorrelation between having been unemployed for 6 consecutive months (relative to being employed during that time) and being 3months delinquent in the current month.

36

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39

For Online Publication

Sara G. Castellanos, Diego Jiménez-Hernández, Aprajit Mahajan, Enrique Seira

Contents

Appendix A. Data OA - 2A.1 Construction of “matched” sample for summary statistics . . . . . . . . . . . . . . . . . . . . . . .OA - 2A.2 Background data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 2A.3 Data Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 3

Appendix B. Credit and Financial Inclusion OA - 5B.1 Are NTB Borrowers Credit Constrained? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 5B.2 Risks and Revenues from Financial Inclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 8B.3 Predicting Default, Revenue, Cancellations and Paid Interest . . . . . . . . . . . . . . . . . . . . .OA - 10B.4 The cost of business stealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 14

Appendix C. Experiment OA - 15C.1 Experiment Details and Randomization Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 15C.2 Minimum Payments Bind for a Substantial Fraction of Borrowers . . . . . . . . . . . . . . . . . .OA - 18C.3 Credit Limits Are Orthogonal to Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 19C.4 Experimental Results: Other Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 20C.5 Comparison of min. payment across treatment arms 3 years after the experiment ended . . . . .OA - 36

Appendix D.Habit formation OA - 37

Appendix E. Comparisons OA - 37

Appendix F. Mechanisms OA - 38F.1 Consequences of default . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OA - 38

Appendix G.Comparison with Compartamos and Azteca OA - 39

OA - 1

Appendix A. Data

A.1 Construction of “matched” sample for summary statistics

This subsection describes how we constructed the sample from Column 4 in Table 1. First, note that, forthe experimental sample in March 2007 (Column 1), Panel B shows that the mean tenure is 68 months with astandard deviation of 54 months. Using the individuals from the experimental sample in (described in Section2) and focusing in March 2007, we construct 50-quintiles for the tenure in months of the oldest credit. Doingso gives us values r1, . . . , r49 where those cardholders whose loan tenure falls between [ri, ri+1) are in the(i+ 1)−th quintile, and we can define r0 and r50 as the min and max values for the tenure to have the first andlast 50-quintile groups defined. By construction, we have the same amount of cardholders in each [ri, ri+1)

region.Next, we restrict to individuals in the credit bureau who had at least one credit card open in June 2010

(i.e. those shown in Column 3). We then drop any individual whose tenure in months of the oldest credit fallsoutside of r0 and r50. Then, for each i = 1, . . . , 50 we define qi as the number of individuals whose loan tenurein June 2010 falls in [ri−1, ri), and define by q∗ = mini qi as the region where we observe the smallest amount ofindividuals. In our data q∗ = 1, 149. Finally, for each i = 1, . . . , 50 we randomly select (without replacement)q∗ individuals whose loan tenure falls between [ri−1, ri). This leaves us with a sample of 57,450 individualsshown in Column 4.

A.2 Background data

Figure OA-7: Creditholders by income in October 2011

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Market data Experiment

Notes: The histogram in dark bars is the income distribution of a random sample of consumers in the credit bureau with at leastone credit card. The light bars shows the corresponding distribution for the experimental sample (using sampling weights). Bothhistograms are censored at 45,000 pesos. Income data is from the IMSS and we were able to match 18 and 13 percent of the experimentaland credit bureau random sample datasets to the IMSS.

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Figure OA-8: Example of Promotional Kiosks

-3-332-3--36away .

• •

A.3 Data Check

We argue the following relation holds in our data:

amount duei,t = amount duei,t−1 + purchasesi,t − paymentsi,t + feesi,t + debti,t × interest ratei (4)

To test such an equation in our data we use observations with positive debt (as the coefficient on theinteraction between debt and interest rate is not identified in the case when debt is zero). The following TableOA-7 summarizes our results. We find that that inferred interest rates match closely with experimental interestrates. This suggests that the debt transition equation (4) above is a good approximation to reality and that thedata on purchases, debt, payments, and fees is consistent. The R2=1 means that the formula is virtually anidentity in the data.

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Table OA-7: Data check

(1)

Amount Duei,t−1 0.996(0.000248)

Paymentsi,t -1.000(0.000363)

Purchasesi,t 1.008(0.00102)

15% x Debti,t 0.179(0.00343)

25% x Debti,t 0.279(0.00356)

35% x Debti,t 0.380(0.00370)

45% x Debti,t 0.476(0.00474)

Feesi,t 0.495(0.00178)

R-squared 1.000Observations 483536

Notes: This table estimates equation (4) by OLS on months with positive debt. That is we estimate the β’s in the following equation:Amount dueit = β0 + β1Amount dueit−1 + β2Paymentsit + β3Purchasesit +

∑k γk Debtit × I(r = k) + β5Feesit + εit, where

k ∈ {15, 25, 35, 45} The coefficients are unconstrained, so a coefficient of payments =-1 for instance is a result and not an imposedconstraint. The same is true of interest rates: the coefficient on I(r = 25%), i.e. γ25 =0.27 being close to 0.25 is a result as well.

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Appendix B. Credit and Financial Inclusion

B.1 Are NTB Borrowers Credit Constrained?

Recent and limited participation in the formal credit sector raises the possibility that NTB clients continueto be credit constrained. Evidence of continuing credit constraints will provide the context for understandingthe experimental treatment effects in the sequel. We test for the existence of credit constraints by examiningdebt responses (in the experimental sample) to increases in credit limits for the study card. If borrowers arenot liquidity or credit constrained, their debt should not respond to exogenous increases in credit limits.61

Conversely, one can view debt (or more generally consumption) responses to changes in credit limits as ev-idence of credit constraints.62 Note, however, increases in borrowing following credit limit expansions for aparticular card could also be consistent with the lack of credit constraints if borrowers replace costlier debt withcheaper debt. We can partly address this problem by examining all (formal sector) debt responses (using theCB data) to credit limit changes. However, since we do not observe informal borrowing, we cannot rule outthe possibility of substitution away from informal loans as a response to changing formal sector credit limits.

First, we use monthly data on debt and credit limits (using the bank data for the experimental sample) toregress one month changes in debt on 12 lagged one month changes in credit limits.63 Let Debtit be the amountof debt held by card i at the end of month t, let Limitit denote the credit limit for account i at the beginningof month t and Xit denotes a set of controls. Following the main specification in Gross and Souleles (2002) weestimate

∆Debti,t = δt +T∑j=0

βj∆Limiti,t−j + γ′Xi,t + εi,t (5)

where ∆ is the first-difference operator and βj represents the incremental increase in debt between month t−1

and t associated with a one peso change in credit limit in period t − j. The scalar parameter θ ≡∑T

j=0 βj

then provides us with a summary measure of the long-run (T month) total effect of credit limit on debt; wereport θ ≡

∑Tj=0 βj for each regression.64 Because the bank evaluates a card for credit-limit changes using pre-

determined durations, cards that had received a credit limit change further back in the past will have a higherpresent probability of a credit limit change than otherwise identical cards that received a credit limit increaserelatively recently. To address concerns that credit-limits change endogenously, we can therefore instrumentlimit changes by the time since the last limit increase, while controlling for the total number of increases in thesample period.65

The results are presented in Table OA-8. In all tables, we adopt the convention of three asterisks denotingsignificance at the .1% level, two asterisks at the 1% significance level and one asterisk at the 5% significancelevel. Panel A uses debit and limit data for just the study card while Panel B uses (changes in ) total credit carddebt (from the CB data) as the dependent variable.66 For Panel B, since we only have annual data, we modifyequation (5) and regress one year changes in debt on one year changes in credit limits (i.e T = 2). Column (1)presents results for the entire experimental sample while the subsequent columns estimate the model on the 9

61Assuming no wealth effects of the increased limits.62See e.g. Deaton (1991), Carroll (1992), Gross and Souleles (2002).63Covariates include time dummies, demographics, credit score in June 2007, as well as indicators for the number of credit changes

during the experiment. Results were robust to including card level fixed effects.64Standard errors were computed using the delta method.65See Gross and Souleles (2002) for the same approach.66Adding non-revolving loans would induce a mechanical effect as debt is equal to the limit for these.

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different strata.First, focusing on the entire sample we find that after 12 months a credit limit increase of 100 pesos for the

study card translates into 32 pesos of additional debt (Row 1). This number remains essentially unchangedwhen we add controls (not reported) while the IV estimate is substantially larger (73 pesos). This propensityto consume out of increases in the credit limit is about thrice as large as the figure for the US and suggests thatthese Mexican borrowers are credit constrained and significantly more so than their US counterparts.67

This conclusion finds further support in the stratum-specific results where we document two main find-ings. First, longer tenure with the bank (controlling for baseline payment behavior) corresponds to lowerestimated responses – for instance borrowers who have had the card for more than two years are on averageless than half as responsive to changes in credit limits relative to those who have been with the bank for lessthan a year. Second, controlling for bank tenure, borrowers with worse baseline repayment behavior are moreresponsive to credit limit changes relative to borrowers with good baseline repayment behavior. For instance,borrowers who have historically paid close to the minimum amount each period are about three times (ormore) as responsive to changes in credit limits relative to borrowers who have historically paid off their entirebalance each month. These results suggest that a shorter tenure with the bank and poor repayment behaviorare in part at least reflective of greater credit constraints.

Finally, in Panel B we estimate equation (5) for the experimental sample using (annual) credit bureau data(with T = 0 — i.e. we only include once lagged credit limit changes) and debt and credit limits are now totaldebt and total credit limit summed across all of the borrower’s formal credit history. This allows us to partlyaddress the issue of credit substitution raised earlier. The results largely confirm the previous panel althoughthe point estimates are now, on average, smaller than earlier. Our overall conclusion from the precedingexercise is that the experimental sample’s response to changes in credit limits are consistent with the existenceof credit constraints and these credit constraints appear to be stronger for borrowers with shorter bank tenureand poorer repayment histories.

67Gross and Souleles (2002) find estimates in the range of 0.11 − 0.15 relative to our baseline estimate of 0.32. Our estimates arealso higher than those obtained by Aydin (2018) who induces experimental variation in credit card limits (in an unnamed Europeancountry) and estimates a response of 0.20 (with T = 9).

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Table OA-8: Suggestive Evidence for Credit Constraints: Cumulative Effect of Credit Limit Changes on Debt

6-11 months 12-23 months 24+ months

All Minimum Two + Full Minimum Two + Full Minimum Two + Full(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Panel A. Bank A’s debt (dependent variable) and Card A’s credit limit (independent variable)Baseline estimate 0.32 0.69 0.41 0.23 0.56 0.47 0.13 0.33 0.13 0.03

(0.04) (0.06) (0.04) (0.03) (0.05) (0.05) (0.02) (0.06) (0.03) (0.01)IV estimate 0.73 2.14 1.24 0.47 1.60 1.06 0.09 0.62 0.52 -0.08

(0.14) (0.32) (0.28) (0.37) (0.28) (0.39) (0.09) (0.19) (0.27) (0.14)

Observations 1,366,035 118,687 143,397 170,791 125,859 145,077 174,305 14,6291 155,290 186,338Mean dependent variable 70 184 102 59 100 55 23 95 43 23

(2292) (3631) (2771) (1756) (2639) (2092) (1163) (2863) (2174) (1272)Mean changes in limit -104 -141 -115 -105 -97 -90 -77 -100 -97 -120

(1460) (1532) (1452) (1486) (1149) (1129) (1177) (1446) (1487) (1956)Mean utilization .52 .72 .59 .39 .68 .58 .4 .64 .53 .3

(2.96) (.34) (3.07) (.33) (3) (3.56) (4.81) (.35) (3.6) (2.82)Median utilization .5 .81 .58 .33 .78 .58 .3 .71 .51 .2

Panel B. Total debt across all cards (dependent variable) and total credit limit across all cards (independent variable)Baseline estimate 0.29 0.37 0.40 0.32 0.42 0.35 0.19 0.29 0.24 0.15

(0.01) (0.03) (0.02) (0.02) (0.03) (0.02) (0.02) (0.02) (0.02) (0.01)IV estimate 0.45 1.17 0.76 0.51 0.84 0.45 0.37 0.38 0.34 0.24

(0.05) (0.12) (0.07) (0.04) (0.09) (0.06) (0.04) (0.07) (0.06) (0.04)

Observations 210,886 24,249 23,473 22,932 23,103 22,560 22,250 23,959 23,789 24,571Mean dependent variable 598 1440 889 549 808 453 258 577 360 198

(4402) (7023) (5220) (3342) (5045) (3886) (2140) (5095) (3769) (2257)Mean changes in limit 657 485 558 722 564 584 744 730 711 770

(2228) (2058) (2163) (2438) (1726) (1807) (2131) (2246) (2285) (2820)Mean utilization .45 .67 .5 .33 .62 .47 .28 .54 .42 .22

(.38) (.42) (.38) (.31) (.39) (.37) (.28) (.37) (.35) (.24)Median utilization .38 .65 .45 .24 .59 .41 .2 .51 .35 .14

Notes: Each cell represents a separate regression and displays estimates of θ ≡∑T

j=0 βj from Equation 5; all regressions include monthdummies. The first row (“Baseline”) in each panel displays estimates from regressions of current debt on past changes in credit limits(equation 5) estimated using OLS. The second row in each panel (“IV”) displays results from estimating the equation using (dummiesfor the) months since the last credit limit change as instrumental variables. For the IV specification equation 5 controls directly forthe total number of credit limit increases and decreases as well. Column (1) estimates include probability weights based on the sizeof each of the strata in the population. Columns (2)-(8) present stratum specific estimates. Both panels use the experimental samplealbeit at different frequencies. Panel A presents results from estimating (5) at the monthly level with T = 12. The dependent variableis the total debt on the study card and the independent variable of interest is the credit limit for the study card. The dependent variablefor Panel B is the total debt across all cards in the credit bureau for the experimental sample and the main independent variable isthe total limit among across all cards. Since we only observe data at the annual level for the credit bureau, Panel B has T = 2. Theinstrument for both panels is months since last credit limit change in the study card only. Standard errors are shown in parenthesesand are clustered at the individual level.

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B.1.1 Variation in Credit Constraints Across Strata

A direct test of whether the strata vary systematically in terms of credit constraints is to estimate equation(5) separately for each stratum and compare the magnitudes of the estimates of θ across strata. The resultsare presented in Table (OA-8) and show that by this metric the stratum with the newest borrowers and thepoorest repayment history (i.e. the “6-11 Month ,Min Payer” stratum) is the most credit constrained and thestratum containing the oldest borrowers with the best ex-ante repayment history (the “24+Month, Full Payer”stratum) is the least constrained. For the former stratum, a 100 peso increase in the credit limit leads to debtincrease of 69 pesos twelve months later, while the corresponding figure for the latter stratum is only 3 pesos(Panel A Row 1).68 This pattern is confirmed across the remaining seven strata: controlling for tenure with thebank, poorer repayment histories are correlated with higher estimates of θ and correspondingly, controlling forbaseline repayment history, increased tenure with the bank is correlated with lower debt responses to creditlimit changes.

B.2 Risks and Revenues from Financial Inclusion

Figure OA-9: Card Exits: Experimental DataCard Closings in Experiment, by Type of Closing

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Notes: This figure plots card closing rates over the course of the experiment for the control group. Card closings are subdivided into(a) bank initiated revocations (i.e. default), (b) (borrower initiated) cancellations, and (c) other reasons (e.g. death of owner). Forcomparison, Figure OA-10 in the online appendix plots the analogous graphs for this figure for two different strata.

68The IV estimates are substantially larger for the most constrained stratum – a 214 peso increase in debt – but unchanged for theleast constrained stratum.

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Figure OA-10: Card Exit during the Experiment: Selected Strata

(a) Full payers with 24+ months with the credit card10

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Notes: These figures plot card exit rates over the course of the experiment for the control group and for two different strata. Cardclosure is subdivided into whether it was a (a) default/revocation, (b) cancellation or (c) closure for some other reason (primarily lostcards or death). The aggregate exit rates (for the entire sample) are in Figure OA-9 in the main paper.

Figure OA-11: Default and Credit Scores

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Notes: This figure plots a kernel regression of default (in May 2009) against credit scores (in June 2007). This forms basis of ourestimate of the likelihood of default used in constructing our bank revenue measure (see Section 2.2).

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Figure OA-12: Robustness: Best and Worse Case Bounds (for αi)

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Notes: Histograms of the revenue measure computed with αi = .05 (low recovery rates) for all borrowers (in brown) and the best casescenario with αi = 0.95 (in pink). The resulting histograms do not vary significantly from the one constructed using estimated valuesof αi for each borrower.

Figure OA-13: Revenue and Credit Scores: By Strata

(a) Distribution of RevenueFull payers with 24+ months with the study card

(“Full,24+M”)

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(b) Distribution of RevenueMin. payment payers with 6-11 months with the study

card (“Min,6-11M”)

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Notes: Figures (a) and (c) represent the distribution of the revenue measure for two different strata (the graph is censored at ±20,000pesos). Figures (b) and (d) display kernel regressions of the revenue measure on credit scores (in June 2007) at the borrower level.Each kernel regression is censored at the 5th and 95th percentile of the corresponding credit score distribution in the given strata.

B.3 Predicting Default, Revenue, Cancellations and Paid Interest

We show the results from predicting revenues, default, cancellations, and which consumers end up payinginterest at least once on Tables OA-9 and OA-10. The results in both Tables focus on the benchmark model, OLSand Random Forests. We use cross validation to fine tune the depth of each tree and the number of minimum

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samples within each leaf in the Random Forest model. For each model we predict the dependent variables (oneat a time) using different sets of covariates. Each panel uses a different information set starting with a minimalset (most closely corresponding to the bank’s information set when it issued the card) to progressively largerones. Panel A includes variables measured at the time of application while Panel B uses the same variablesbut as observed in March 2007 (i.e. after the card was awarded) as well as the credit score in June 2007.69

Panel C adds purchases, payments and total debt in March 2007 yielding the richest set of covariates. Themost successful model, the Random Forest, has an out-of-sample R2 of 0.06 in Panel A and 0.17 in Panel C.For revenues, the out-of-sample root MSE is 7,204 pesos for Panel A and 4,474 for Panel C, which are aboutthe same as the intercept-only model. Performance improves somewhat in Panel C so that interactions withthe bank (measured here in terms of payment, purchase and debt history) are useful indicators of revenue.We note, however, that even the best performing ML tool does not significantly out-perform the simplestintercept-only model on all measures. We also attempted to predict default and cancellations using the samecovariates and strategy.

The general message from the differing information sets and methods is the same – it is quite difficultto predict which NTB borrowers will generate revenues for the bank and that adding a range of subsequentinformation (unavailable to the bank at the time of application such as payments, purchases and debt) doesimprove prediction, but only modestly.70 A caveat is in order. We only observe successful applicants (ratherthan the entire applicant pool) and the prediction exercise is carried out on this (presumably positively) se-lected sample. This is clearly a limitation, but even this screened sample is by no means homogeneous or riskfree and as we show above this risk is hard to predict. Even though the bank presumably screened as best itcould, the result appears unsatisfactory – that the bank decided to shut down the study card provides furtherevidence of this.

69The variables include zip code, marital status, sex, date of birth, number of prior loans, number of prior credit cards, number ofpayments in the credit bureau, number of banks interacted with, payments in arrears, date of previous default and tenure with thecredit bureau.

70However, see e.g. Björkegren and Grissen (2017) that also uses machine learning methods to predict loan default with morepromising results (using borrowers’ mobile phone usage patterns).

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Table OA-9: Predicting Revenue and Default with Different Information Sets

Revenue Default

BenchmarkLinear Random

BenchmarkLinear Random

Regression Forest Regression Forest(1) (2) (3) (4) (5) (6)

Panel A. Public information available at the moment of applicationρ(predicted,realized) 0.00 0.04 0.28 0.00 0.45 0.45Out of sample root MSE 7452 7444 7204 0.43 0.38 0.38Out of sample MAE 5198 5136 4954 0.32 0.29 0.28Out of sample R-squared 0.00 0.00 0.06 0.00 0.19 0.20AUC - ROC Curve - - - 0.50 0.79 0.79

Panel B. March 2007 public informationρ(predicted,realized) 0.00 0.05 0.28 0.00 0.45 0.45Out of sample root MSE 7399 7389 7149 0.43 0.38 0.38Out of sample MAE 5161 5096 4914 0.32 0.29 0.28Out of sample R-squared 0.00 0.00 0.06 0.00 0.19 0.20AUC - ROC Curve - - - 0.50 0.79 0.79

Panel C. March 2007 public and private informationρ(predicted,realized) 0.00 0.33 0.41 0.00 0.46 0.49Out of sample root MSE 7409 7023 6765 0.43 0.38 0.37Out of sample MAE 5169 4695 4474 0.32 0.28 0.26Out of sample R-squared 0.00 0.11 0.17 0.00 0.21 0.24AUC - ROC Curve - - - 0.50 0.81 0.81

Note: MODELS: We predict revenues and default using a range of standard machine learning methods including Support Vector Machines, NeuralNetworks, Boosting, and Random Forests. Model parameters are tuned using out-of-sample (OoS) cross validation. The table shows results for theRandom Forest in columns (3) and (6) since it achieved the smallest out-of-sample mean squared error across all the methods mentioned above.Columns (1) and (2) present results for a constant only model and a linear regression model to provide benchmarks. INPUTS: The Table contains threepanels, which differ in the input variables. Panel A uses variables measured at the moment of application. These include the state, applicant/borrowerzip code, marital status, gender, date of birth, number of prior loans, number of prior credit cards, number of payments in the credit bureau, numberof banks interacted with, number of payments in arrears, number of payments in arrears specifically for credit cards, length of presence (in months)in the credit bureau, the date of the last time the borrower was in arrears, and the date of the last time the borrower was in arrears for any creditcard. Panel B uses all variables from Panel A, but measured in March 2007, i.e. after our experimental cards were awarded. We are thus easing thelender’s prediction problem by including information unavailable to the lender at the time of application. In addition, we also include a the creditscore (measured in June 2007) – this is our earliest credit score measure). Panel C adds further information (that was likewise unavailable to lender atthe time of application): beside using all variables in Panel B, it adds purchases, payments, debt, and amount due from the study card, all measured inMarch 2007. GOODNESS OF FIT: We partition the control group into a training sample composed by cardholders who have had the experimental cardfor more than one year (i.e. those that belong to the 12-23M and 24+M strata and all payment behaviors) and a test sample composed by individualswho have had the experimental card for more than 6 months but less than a year (i.e. those that belong to the 6-11M strata and all payment behaviors).We estimate the 3 models (for each panel) using the training sample, and then evaluate each model by comparing its predicted predicted outcome tothe true observed outcome in the test (holdout) sample. The cells above show different goodness-of-fit measures for each model and set of inputs. Thefirst row in each panel represents the correlation between the predicted value (in the case of discrete variables we use predicted probabilities) and therealized value in the test sample. The second row presents the mean squared error, the third shows the mean absolute error, the fourth displays the“R-squared” (defined as 1 minus the ratio of the variance of the prediction errors relative to the variance of the dependent variable), and the fifth rowshows the area under the ROC curve, used for indicator outcomes.

Regarding AUCs for default, They are lower than those documented in several studies and somewhathigher than those found in for credit cards in the US71, but lower than those from loans in Australia, Japan,and Poland;72 lower than those in the housing market in the US;73 lower than those for credit default swapsin the US;74; higher than those to predict repayment using cellphone data in an unnamed South Americancountry;75 and higher than those for a micro-finance lender in Bosnia Herzegovina.76

71Khandani et al. (2010) shows AUCs between 0.89 to 0.95 for credit cards in the US in a similar time period to our paper72Ala’Raj and Abbod (2016) reports AUCs of 0.80, 0.94, 0.93, 0.77 and 0.84 for loan data from Germany, Australia, Japan, Iran, and

Poland, respectively. Abellán and Mantas (2014) reports AUCs of 0.93, 0.93 and 0.78 for loan data from Japan, Australia, and Germany,respectively.

73Fuster et al. (2017) reports an AUC of 0.86 for US mortgage data from 2009 to 2014.74Luo et al. (2017) reports AUCs around 0.92 for credit default swaps on 2016.75Björkegren and Grissen (2017) reports AUCs between 0.61 and 0.76.76Van Gool et al. (2012) reports an AUC of 0.71 for a mid-sized Bosnian microlender.

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Table OA-10: Predicting cancellations and paid interest

Cancellations Paid interest

BenchmarkLinear Random

BenchmarkLinear Random

Regression Forest Regression Forest(1) (2) (3) (4) (5) (6)

Panel A. Public information available at the moment of applicationρ(predicted,realized) 0.00 0.14 0.15 0.00 0.42 0.44Out of sample root MSE 0.35 0.35 0.34 0.50 0.45 0.45Out of sample MAE 0.27 0.26 0.26 0.50 0.42 0.42Out of sample R-squared 0.00 0.02 0.02 0.00 0.17 0.18AUC - ROC Curve 0.50 0.62 0.62 0.50 0.75 0.75

Panel B. March 2007 public informationρ(predicted,realized) 0.00 0.14 0.15 0.00 0.41 0.44Out of sample root MSE 0.35 0.35 0.35 0.50 0.45 0.45Out of sample MAE 0.27 0.26 0.26 0.50 0.42 0.42Out of sample R-squared 0.00 0.02 0.02 0.00 0.17 0.18AUC - ROC Curve 0.50 0.61 0.62 0.50 0.75 0.75

Panel C. March 2007 public and private informationρ(predicted,realized) 0.00 0.26 0.31 0.00 0.45 0.52Out of sample root MSE 0.35 0.34 0.33 0.50 0.44 0.42Out of sample MAE 0.27 0.24 0.23 0.50 0.41 0.38Out of sample R-squared 0.00 0.07 0.10 0.00 0.20 0.27AUC - ROC Curve 0.50 0.66 0.70 0.50 0.78 0.80

Notes: MODELS: We predict cancellations using a range of standard machine learning methods including Support Vector Machines,Neural Networks, Boosting, and Random Forests. Model parameters are tuned using out-of-sample cross validation. The table showsresults for the Random Forest in column (3) since it achieved the smallest out-of-sample mean squared error across all the methodsmentioned above. Columns (1) and (2) present results for a constant only model and a linear regression model as benchmarks.INPUTS: The Table contains three panels, which differ in the input variables. Panel A uses variables measured at the moment ofapplication. These include the state, applicant/borrower zip code, marital status, gender, date of birth, number of prior loans, numberof prior credit cards, number of payments in the credit bureau, number of banks interacted with, number of payments in arrears,number of payments in arrears specifically for credit cards, length of presence (in months) in the credit bureau, the date of the last timethe borrower was in arrears, and the date of the last time the borrower was in arrears for any credit card. Panel B uses all variablesfrom Panel A, but measured in March 2007, i.e. after our experimental cards were awarded. We are thus easing the lender’s predictionproblem by including information unavailable to the lender at the time of application. In addition, we also include a the credit score(measured in June 2007) – this is our earliest credit score measure). Panel C adds further information (that was likewise unavailable tolender at the time of application): beside using all variables in Panel B, it adds purchases, payments, debt, and amount due from thestudy card, all measured in March 2007. GOODNESS OF FIT: We randomly partition the control group into two samples: a trainingsample composed by cardholders who have had the experimental card for more than one year (i.e. those that belong to the 12-23Mand 24+M strata and all payment behaviors) and a test sample composed by individuals who have had the experimental card for morethan 6 months but less than a year (i.e. those that belong to the 6-11M strata and all payment behaviors). We estimate the 3 models(for each panel) using the training sample, and then evaluate each model by comparing its predicted predicted outcome to the trueobserved outcome in the test sample. The cells above show different goodness-of-fit measures for each model and set of inputs. Thefirst row in each panel represents the correlation between the predicted value and the realized value in the test sample. The secondrow presents the mean squared error, the third shows the mean absolute error, the fourth displays the “R-squared” (defined as 1 minusthe ratio of the variance of the prediction errors relative to the variance of the dependent variable), and the fifth row shows the areaunder the ROC curve, used for indicator outcomes.

OA - 13

B.4 The cost of business stealing

Table OA-11: Quantifying First Lender Loss

counterfactual revenueplacebo estimation on

non attriters

estimated predicted realbiasrevenue revenue

(1) (2) (3) (4) (5) (6)

Panel A. Switcher DefinitionClosed exp. card and opened w/ other bank in +- 6m yes yes yes - - -No cards opened between May/03 and Oct/06 no yes yes - - -Experimental card was first card no no yes - - -

Panel B. Estimation ResultsIndividuals in switcher definition 924 365 178 200 200 200Potential controls 17,076 17,365 17,882 9,945 9,945 9,945Mean loss by account 4,324 3,783 4,141 6,837 6,945 -44Confidence interval for mean loss (4044, 4785) (3513, 4335) (3639, 5008) [6126, 7522] [6065, 7918] [-852,519]

Notes: This table estimates the cost (to Bank A) from losing NTB clients to other banks using only the control group (18,000 borrowers).We focus on borrowers who satisfy 3 conditions. (a) They cancelled the study card during the 26 month study; (b) They opened a cardwith another bank within a twelve month period (± 6 months) of cancellation; (c) They did not open any other cards between May2003 and October 2006 (i.e. until 6 months before the experiment started); and (d) the study card was their first credit card. Columns (1)to (3) use a subset of these conditions as detailed in Panel A. The number of individuals who jointly satisfy these criteria are defined asswitchers and are detailed in Panel B. For each of these individuals, we compute how much revenue they would have provided BankA had they not switched. This counterfactual is calculated using a matching estimator (defined in Section 3.2) that pairs the switcheri that closed the study card at time t with 10 “control” clients (j1, . . . , j10) from the pool of non-switchers with an active study cardat t. The matching is done using the Mahalanobis distance (on a vector of observables detailed next) from the switching client i inperiod t− 1. We require an exact match on stratum so we are using borrowers from the same stratum to serve as counterfactuals. Theremaining matching variables are credit limit in t−1, purchases in t−1, payments in t−1, debt in t−1, and revenue from March 2007through period t−1. Having construnted the counterfactuals (j1, . . . , j10), we then impute as i’s foregone revenue the average revenuegenerated by (j1, . . . , j10) from t through May 2009. If any of the counterfactuals exits, their subsequent revenue is zero (followingequation 1). We carry out this exercise for every switcher and present the average foregone revenue (and associated standard errorscomputed using sub-sampling in parentheses) of the mean in Panel B, columns (1)-(3). We use sub-sampling (Politis et al. (1999)) sincethe bootstrap is inconsistent for matching based es timators (see Abadie and Imbens, 2008). As detailed Panel A, the columns differ inthe definition of a switcher. Columns (4) to (6) are a placebo estimation exercise to assess the validity of our estimation results. We takethe 10,145 individuals from the control group who do not exit during the experiment and randomly assign 200 of them to be switcherswith an artificial cancellation date randomly assigned between March 2007 and May 2009. Since we observe the true revenue for these200 “switchers”, we can use this exercise to compare the revenue from our estimation to the actual revenue for these borrowers. Werepeat the placebo exercise 100 times.Column (4) shows the average predicted revenue “foregone” for those in the artificial switchers.Column (5) shows the real revenue “foregone” from the data. Column (6) shows the difference between the predicted and the truerevenue. The numbers in squared brackets report the 5th and 95th percentiles out of the 100 repetitions.

OA - 14

Appendix C. Experiment

C.1 Experiment Details and Randomization Check

Table OA-12: Experimental Design

Panel A: Stratification

Full-balance payer Minimum payer Part-balance payer Total6 to 11 months 18,000 18,000 18,000 54,00012 to 23 months 18,000 18,000 18,000 54,000

24+ months 18,000 18,000 18,000 54,000Total 54,000 54,000 54,000 162,000

Panel B: Sample Sizes for Arms Within Strata

Interest Rate Minimum payment

10% 5%

15% 2000 200025% 2000 200035% 2000 200045% 2000 2000

Control 2,000

Table OA-13: Sampling weights

Cardholder’s payment behaviorTotal

Minimum payer Part-balance payer Full-balance payer(1) (2) (3) (4)

Months of credit card use6 to 11 months 9.8 1.6 0.6 1212 to 23 months 10.7 1.7 0.7 1324+ months 61.5 9.8 3.8 75

Total 82 13 5 100

OA - 15

Figure OA-14: Timeline for the Experiment

0. Strata information:

Strata variables recorded.

1. Bank data:

Monthly card level data from 03/07 to 05/09.

2. Credit Bureau data:

Loan level data matched to experimental sample for 06/07 to 06/10, annually.

Loan-level data for 06/10 representative of the entire credit bureau population.

3. Social security data:

Individual-level, monthly information from 10/10 to 05/14.

2007 2008 2009 2010 2011 2012

Notes: This figure presents a timeline for the experiment. The data for the 9 experimental strata was recorded in January 2007. Datafrom the experiment is provided monthly for each card from March 2007 to May 2009. We use CB information for the experimentalsample, which is provided to us in 4 snapshots: June 2007-2010. The full description of the experiment is in Section 4.1.

OA - 16

Tabl

eO

A-1

4:R

ando

miz

atio

nC

heck

-Bas

elin

est

atis

tics

for

Mar

ch20

07

CTR

r=

15%

r=

25%

r=

35%

r=

45%

Tota

lP-

valu

eO

bser

vati

ons

mp

=5

%m

p=

10%

mp

=5

%m

p=

10%

mp

=5

%m

p=

10%

mp

=5

%m

p=

10%

(1)

(2)

(3)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

Pane

lA.A

llob

serv

atio

nsA

ge39

3939

3939

3939

3939

390.

7016

0,93

5(6

)(6

)(6

)(6

)(6

)(6

)(6

)(6

)(6

)(6

)Fe

mal

e(%

)47

4746

4847

4848

4747

470.

6316

1,87

8(5

0)(5

0)(5

0)(5

0)(5

0)(5

0)(5

0)(5

0)(5

0)(5

0)M

arri

ed(%

)64

6564

6565

6565

6465

650.

8615

7,82

2(4

8)(4

8)(4

8)(4

8)(4

8)(4

8)(4

8)(4

8)(4

8)(4

8)D

ebt

1,19

11,

195

1,18

41,

259

1,20

21,

299

1,11

11,

136

1,20

81,

198

0.22

161,

590

(3,3

68)

(3,4

68)

(3,4

02)

(3,7

44)

(3,5

59)

(3,7

42)

(3,2

45)

(3,4

57)

(3,6

69)

(3,5

21)

Purc

hase

s33

333

235

234

432

935

232

835

132

433

80.

4316

1,59

0(1

,041

)(9

75)

(1,1

45)

(1,0

69)

(964

)(1

,016

)(1

,014

)(1

,056

)(9

09)

(1,0

23)

Paym

ents

708

694

762

722

704

704

704

698

703

711

0.77

161,

590

(1,4

57)

(1,2

92)

(1,8

78)

(1,5

41)

(1,3

91)

(1,3

59)

(1,5

87)

(1,3

02)

(1,3

52)

(1,4

73)

Cre

ditl

imit

7,81

47,

867

7,93

77,

853

7,92

77,

999

7,73

97,

925

7,84

87,

879

0.61

161,

590

(6,0

64)

(6,0

03)

(6,2

79)

(5,9

48)

(6,2

26)

(6,2

69)

(5,6

32)

(6,4

03)

(6,1

86)

(6,1

17)

Del

inqu

ent(

%)

1.4

1.8

1.6

1.9

1.4

1.7

1.8

1.5

1.5

1.6

0.37

161,

590

(11.

9)(1

3.2)

(12.

7)(1

3.5)

(11.

7)(1

3.0)

(13.

3)(1

2.1)

(12.

1)(1

2.6)

Pane

lB.E

xclu

ding

attr

iters

Age

3939

3939

3939

3939

3939

0.35

96,9

28(6

)(6

)(6

)(6

)(6

)(6

)(6

)(6

)(6

)(6

)Fe

mal

e(%

)46

4847

4748

4949

4647

470.

3297

,163

(50)

(50)

(50)

(50)

(50)

(50)

(50)

(50)

(50)

(50)

Mar

ried

(%)

6565

6664

6566

6665

6665

0.78

94,8

35(4

8)(4

8)(4

8)(4

8)(4

8)(4

7)(4

7)(4

8)(4

7)(4

8)D

ebt

805

728

747

811

844

871

680

713

828

780

0.13

97,2

48(2

,693

)(2

,764

)(2

,775

)(3

,099

)(3

,133

)(3

,027

)(2

,533

)(2

,591

)(3

,225

)(2

,882

)Pu

rcha

ses

386

379

412

395

376

395

367

386

358

384

0.46

97,2

48(1

,045

)(1

,051

)(1

,237

)(1

,163

)(1

,037

)(1

,092

)(1

,092

)(1

,152

)(9

82)

(1,0

99)

Paym

ents

752

715

769

727

711

717

690

686

733

722

0.33

97,2

48(1

,417

)(1

,264

)(1

,701

)(1

,342

)(1

,227

)(1

,291

)(1

,390

)(1

,234

)(1

,345

)(1

,363

)C

redi

tlim

it7,

865

7,89

77,

916

7,93

27,

933

7,94

17,

688

7,78

27,

757

7,85

90.

7197

,248

(6,2

91)

(5,9

77)

(6,3

19)

(6,0

21)

(6,1

89)

(6,2

91)

(5,4

30)

(5,9

30)

(6,1

47)

(6,0

70)

Del

inqu

ent(

%)

0.2

0.2

0.4

0.2

0.1

0.2

0.2

0.2

0.2

0.2

0.11

97,2

48(3

.9)

(4.9

)(6

.2)

(4.5

)(2

.9)

(5.0

)(4

.6)

(4.3

)(4

.9)

(4.7

)

Not

es:

Col

umns

(1)t

o(1

0)ta

bula

teth

em

ean

(sta

ndar

dde

viat

ion

inpa

rent

hese

s)fo

rth

eva

riou

str

eatm

enta

rms

inth

eex

peri

men

t.T

hest

anda

rder

ror

for

the

mea

nes

tim

ates

can

beco

mpu

ted

bydi

vidi

ngth

est

anda

rdde

viat

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byth

e(s

quar

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the)

num

ber

ofin

divi

dual

sin

each

trea

tmen

tarm

.Tim

e-va

ryin

gva

riab

les

are

mea

sure

dhe

reat

the

begi

nnin

gof

the

expe

rim

ent.

Pane

lAin

clud

esal

lind

ivid

uals

,whe

reas

Pane

lBex

clud

esth

ose

indi

vidu

als

who

exit

the

expe

rim

enta

tany

poin

t.C

olum

n(1

1)sh

ows

the

mea

nan

dst

anda

rdde

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ions

ofth

eco

mpl

ete

sam

ple.

Col

umn

(12)

show

sth

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valu

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ate

stof

the

null

hypo

thes

isth

atal

lmea

nsfr

om(1

)–(1

0)ar

eeq

ual.

OA - 17

C.2 Minimum Payments Bind for a Substantial Fraction of Borrowers

Figure OA-15: Payment as a fraction of debt before the experiment

(a) Mar/07 - all treatment arms

0.14

0.08

0.39

0.12

0.06

0.040.02 0.02 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00

0.07

0.1

.2.3

.4Fr

actio

n of

car

dhol

ders

0 .1 .2 .3 .4 .5Payment as proportion of amount due

(b) Oct/07 - treatment arms with mp = 5%

0.14

0.07

0.35

0.10

0.05

0.030.02

0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00

0.15

0.1

.2.3

.4Fr

actio

n of

car

dhol

ders

0 .1 .2 .3 .4 .5Payment as proportion of amount due

(c) Oct/07 - treatment arms with mp = 10%

0.15

0.02

0.03

0.09

0.32

0.06

0.04 0.030.02 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00

0.17

0.1

.2.3

.4Fr

actio

n of

car

dhol

ders

0 .1 .2 .3 .4 .5Payment as proportion of amount due

Notes: We plot monthly payment divided by the amount due. In Figure (a) this is the ratio of monthly payments in April 2007 andthe amount due in the March 2007 statement. In Panels (b) and (c) we examine the ratio of monthly payments in October 2007 to theamount due in the September 2007 statement. We right-censor all figures at 0.5, so the rightmost bin for each panel includes thosewhose payment ratio is 0.5 or higher. The leftmost bin starts at 0, and all bins have a width of 0.25. The number above each binrepresents the fraction of cardholders in the given bin. The variable in the x-axis is only an approximation to the minimum paymentsince the minimum payment may include some fees or discounts that we do not observe.

OA - 18

C.3 Credit Limits Are Orthogonal to Randomization

Table OA-15: Credit Limits and Treatment Arms

Card Limit(1) (2)

I:15% P:5% 44.791 37.083(210.287) (210.174)

I:15% P:10% 41.241 43.153(217.952) (217.839)

I:25% P:5% -83.622 -89.419(209.235) (209.124)

I:25% P:10% -108.242 -102.967(210.609) (210.506)

I:35% P:5% 119.108 115.921(220.234) (220.135)

I:35% P:10% -312.358 -305.073(208.315) (208.206)

I:45% P:10% -226.953 -216.079(208.907) (208.802)

Constant 11778.035 11779.590(157.032) (156.951)

Time fixed effects No YesObservations 3,201,085 3,201,085p-value Treatments 0.438 0.486p-value Strata 0.000 0.000R-squared 0.021 0.030Dependent Variable Mean 11157 11157

Notes: Each column represents a different regression. The dependent variable is credit limit in month t for individual i. Independentvariables comprise treatment and strata indicators. Column (2) adds month fixed effects.

Figure OA-16: Credit Limits by Month by Treatment Arms

7.5

8.5

9.5

10.5

11.5

12.5

13.5

cred

it lim

it (th

ousa

nds)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

MP,r (%): 5, 15 10, 15 5, 25 10, 255, 35 10, 35 5, 45 10, 45

OA - 19

C.4 Experimental Results: Other Outcomes

C.4.1 Experiment: Raw Data

Figure OA-17: Effect of Minimum Payment Variations

(a) Interest paying debt

1000

1200

1400

1600

1800

2000

debt

(MX

N p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

MP (%): 5 10

(b) Purchases

300

400

500

600

700

800

purc

hase

s (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

MP (%): 5 10

(c) Payments

600

700

800

900

1000

paym

ents

(MX

N p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

MP (%): 5 10

Note: The figures plot different outcomes over time separately for borrowers in the 5% and 10% minimum payment arms (poolingover the interest rate arms).

OA - 20

Figure OA-18: Effect of Interest Rate Variation

(a) Interest paying debt

1000

1200

1400

1600

1800

debt

(MX

N p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

r (%): 15 25 35 45

(b) Purchases

300

400

500

600

700

800

purc

hase

s (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

r (%): 15 25 35 45

(c) Payments

600

700

800

900

paym

ents

(MX

N p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

r (%): 15 25 35 45

Note: The figures plot different outcomes over time separately for borrowers in each of the four interest rate arms (pooling over theminimum payment arms).

OA - 21

C.4.2 Default heterogeneous effects

Figure OA-19: Default/Revocation and Client Initiated Cancellations: by Strata

-0.06

-0.04

-0.02

0.00

0.02

0.04

Tre

atm

ent E

ffect

(pr

op)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: interest rateDependent variable: cumulative cancellations

-0.06

-0.04

-0.02

0.00

0.02

0.04

Tre

atm

ent E

ffect

(pr

op)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: minimum paymentDependent variable: cumulative cancellations

-0.05

0.00

0.05

Tre

atm

ent E

ffect

(pr

op)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: interest rateDependent variable: cumulative default

-0.05

0.00

0.05

Tre

atm

ent E

ffect

(pr

op)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: minimum paymentDependent variable: cumulative default

Notes: This Figure is analogous to Figure 5 but estimated separately for two strata. The dark triangles correspond to the “24m+” strataand the light diamonds correspond to the ‘6-11m” strata.

C.4.3 Debt, Purchases and Payments: Methodology

In Section 3.2 card exit was an outcome of interest in itself; here we view card exit as a threat to the in-ternal validity. Specifically, we wish to account for card exit as we examine the effect of the experimentalinterventions on debt, purchases and payments. We attempt to address attrition in a number of ways: First,we implement Lee (2009) and present upper and lower bounds on treatment effects that account for attrition.These bounds are generally wide but for the most part still informative. Second, we present month-by-monthtreatment effects and because card-exit is low in the initial months, our short-term estimates are much lessaffected by attrition bias. Finally, in some cases (i.e. for card cancellations) it seems plausible to impute a valueof zero to outcomes in the periods after card exit. Such a strategy is useful when we are interested in the effectsof the treatment on the outcome without distinguishing between the extensive and intensive margins.

We present both short-term (at the six month horizon) as well as long-term effects (after 26 months atthe end of the experiment). We also present month-by-month treatment effects for each of the 26 months ofthe experiment.77 In addition, when useful, we also examine treatment effect heterogeneity by presentingstratum-specific treatment effects for three strata – (a) the “Full, 24M+” stratum comprising borrowers whohad been with the bank for at least 24 months before January 2007 and had always paid their bills in full (4%

of the population) (b) the “Min, 6-11M” stratum consisting of borrowers who had been with the bank for lessthan a year before January 2007 and had the poorest repayment history78 (10% of the population) and(c) the

77These are currently presented in graphical form. Tables available upon request.78viz. their average payments prior to January 2007 were less than 1.5 times the average minimum payments during this period.

OA - 22

“Min, 24M+” stratum comprising the longest term borrowers in the poorest repayment category (62% of thepopulation and the largest stratum).

For each estimand we present point estimates and account for attrition using bounds. We view attrition intwo distinct ways and thus provide two sets of bounds – first, we consider all card exits regardless of reason(i.e. cancellations, revocations and the other category) as attrition. Second, we set all post-exit outcomes forcard cancellers to zero and only consider the defaulters and other category of card exits to be attriters. Thelatter strategy is arguably justified if we are willing to conflate treatment effects on the extensive and intensivemargins. Further, since card cancellers have chosen to set purchases, payments and debt to zero by exiting thesystem one can plausibly set those outcomes to zero for cancellers rather than missing.79

We estimate the full set of treatment effects in the tables but to simplify exposition we focus on only twocontrasts in the discussion here: (a) The effect of an interest rate decrease from 45% to 15% for borrowers witha minimum payment of 5% (the (45%, 5%) arm vs the (15%, 5%) arm). (b) The effect of a minimum paymentincrease from 5% to 10% for borrowers who faced an APR of 45% (the (45%, 5%) arm vs the (45%, 10%) arm).

Treatment effects for other arms are provided in some cases and the full set of results are available onrequest. For both the short- and long-run results we estimate regressions of the form

Yi =7∑j=1

βjTji +9∑s=1

δsSji + εi (6)

where Yi is the outcome measured either six months after the experiment began or in the last month of theexperiment. The {Tji}7j=1 are treatment dummies for each of 7 intervention arms. The omitted arm is the(MP = 5%, r = 45%) arm since it is the group with terms closest to the status quo and we do not use thecontrol group.80 We include strata dummies {Sji}9j=1 and probability weights in all specifications.81

We also estimate month-by-month treatment effects throughout the experiment. In the interest of brevitywe restrict discussion to the two main contrasts above. In particular, we estimate separately for t = 1 . . . 26

Yit = α1t + β1tT(15%,5%)i + ν1it (7)

Yit = α2t + β2tT(45%,10%)i + ν2it (8)

and in both cases the excluded arm is the (45%, 5%) arm.82 We then graph the estimates of β1t and β2t againsttime along with the corresponding Lee bounds in Figure OA-20. This is a parsimonious way of presenting thenumerous treatment effects as well as allowing the reader to trace the evolution of the treatments over time.In most of the graphs, the bounds are typically tight for the first 6 months – reflecting limited attrition – andthe point estimates at six months are of the same sign and typically the same order of magnitude as the longterm (26 month) effects. Having described the general methodology we next turn to describing the effects ofthe interventions – first on debt and then on purchases, payments and fees.

79A similar argument is harder to justify for defaulters.80As mentioned earlier, the issue with the control arm is that we do not observe the different interest rates faced by borrowers in the

arm.81Alternatively we estimate treatment effects stratum-by-stratum and use the stratum weights to arrive at the treatment effect. This

is equivalent to a regression of the outcome on the treatment indicator using probability weighting. The results from this exercise werevery similar to those presented here and are omitted.

82We do not include stratum fixed effects in these regressions in order to present the corresponding Lee bounds in a straightforwardmanner. In the appendix we construct Lee bounds conditional on strata and use stratum weights to arrive at unconditional bounds.The results are qualitatively similar and so we focus discussion on the simpler estimator.

OA - 23

Figure OA-20: Treatment effect estimates

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

Trea

tmen

t Effe

ct (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: interest rateDependent variable: debt

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

Trea

tmen

t Effe

ct (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: minimum paymentDependent variable: debt

-200.00

-100.00

0.00

100.00

200.00

300.00

Trea

tmen

t Effe

ct (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: interest rateDependent variable: purchases

-200.00

-100.00

0.00

100.00

200.00

300.00

Trea

tmen

t Effe

ct (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: minimum paymentDependent variable: purchases

-400.00

-200.00

0.00

200.00

400.00

Trea

tmen

t Effe

ct (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: interest rateDependent variable: payments

-400.00

-200.00

0.00

200.00

400.00

Trea

tmen

t Effe

ct (M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: minimum paymentDependent variable: payments

-20.00

-10.00

0.00

10.00

20.00

Trea

tmen

t Effe

ct (p

rop)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: interest rateDependent variable: fees incurred

-20.00

-10.00

0.00

10.00

20.00

Trea

tmen

t Effe

ct (p

rop)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Treatment: minimum paymentDependent variable: fees incurred

Notes: The left side of the panel shows the effect of increasing the minimum payment to 10% relative to the 5% group. The right side of the panel

shows the effect of decreasing the interest rate from 45% to 15%. For each month t in the experiment, we run yit = αt + βtTi + δs + εit with treatment

being either (45% IR, 10% MP – left side) or (15% IR, 5% MP – right-side) compared to the (45% IR, 5% MP) arm. Dependent variables are – total debt,

monthly purchases, monthly payments, and fees. We also plot Lee bounds (Lee, 2009) for debt, purchases, and payments (though for computational

reasons we do could not include strata dummies δs for the bounds).

OA - 24

C.4.4 Debt: Effect of Interest Rate Decrease

Debt responses to the interest rate changes follow an interesting and, at first-glance, a somewhat counter-intuitive pattern. Figure OA-20 show that interest rate increases result in a steady, gradual decline in debt(even after accounting for attrition). At the six-month mark, with relatively limited attrition, the impliedelasticity bounds are relatively tight at [0.28, 0.42].83 The bounds begin to widen after the first year but remainconsistently negative and even the upper bounds suggest reasonable sized treatment effects. At endline, theupper bound is a decline of 474 pesos and the lower bound is a decline of 1576 pesos. These final bounds implya strictly positive elasticity ranging from +0.34 to +1.12 respectively. Replacing missing values with zeros forcard cancellers provides similar results though the upper bound is now tighter at +0.74. These results suggesta robust, negative effect of interest rate reductions on total debt.84

The treatment effects for the other intermediate treatment arms are in line with these results. We comparedebt for the (45, 5) group to the (r, 5) group where r ∈ {25, 35} and debt in the (45, 10) group to the (r, 10)

group where r ∈ {15, 25, 35}. The five ITT estimates are all comparable to the estimate above.85 The impliedelasticities of debt with respect to the interest rate from the five other ITT estimates thus are also in line withthe elasticities from the primary contrast.86

The negative effect of interest rate declines on debt seems counter-intuitive since borrowers appear to re-spond to price (interest rate) declines by decreasing quantities (debt). We explore this further by examining theeffect of interest rates on purchases, payments and fees which together mechanically determine debt. In Ap-pendix C.4.6 and C.4.8 we establish three facts about these outcomes. First, interest rate declines have inconclu-sive effects on purchases with the Lee bounds for the long-term effect being a relatively wide [−0.38,+0.25].87

Second, monthly payments declined modestly in response to the interest rate decreases with the long-termbounds estimated to be [+0.04,+0.39].88 Third, interest rate declines have a modest negative effect on fees (theLee bounds for the implied elasticity are [+0.15,+1.22]).

Jointly, these facts suggest that the relatively large negative debt response to interest rate declines arisesfrom the fact that lower interest rates result in debt outstanding being compounded at a correspondingly lowerrate.89 This decline more than offsets any increase in purchases as well as the decline in monthly paymentsobserved earlier. To summarize, there is a fairly robust, though moderate, decline in total debt outstanding asa result of the interest rate decrease.C.4.5 Debt: Effect of Minimum Payments

Debt response to the minimum payment increase follows an interesting pattern. Figure OA-20 show thatdebt increases markedly in the third and fourth month of the experiment, increasing by almost 750 pesos byJune 2007. However, there is an similarly precipitous decline soon after with the increase being wiped out by

83Recall that the interest rate manipulation envisaged here is a decline from 45% to 15% so a resultant decrease in debt will result ina positive elasticity.

84Other papers examining examining debt responses to interest rate variation are Karlan and Zinman (2017), Attanasio et al. (2008)and Dehejia et al. (2012) who estimate debt elasticities in Mexico, the United States, and Bangladesh respectively. In all these papersdeclines in interest rates are associated with increases in debt though the magnitudes vary considerably. Attanasio et al. (2008) cannotreject that the elasticity is zero while the three-year elasticity for Karlan and Zinman (2017) is -2.9; Dehejia et al. (2012) provide estimatesin the range of [−0.73.− 1.04].

85For the (45, 5) vs the (15, 5) arm.86Figure OA-21 shows the variation in the treatment effects across strata. Debt for the stratum ex-ante least likely to be liquidity

constrained – the “Full,24M+” borrowers– does not respond at all to the changes in interest rates while the effects are strongest for thestratum ex-ante most likely to be liquidity constrained – the “Min,12M–” borrowers.

87The short-term effects have tighter bounds of [−0.38,−0.18] that suggest modest increases in purchases. More details are in TableOA-17.

88Bounds for the short-term are qualitatively similar at [+0.06,+0.24]. See Table OA-18 for more details.89By large we mean relative to the purchases, payments and fees responses.

OA - 25

September so that the six-month effects are very small – the bounds for the implied elasticities are quite smallat [0.02, 0.08].

Part of the increase in debt in the first months of the experiment appears to arise from late payment fees.90

Following that, debt decreases gradually for the rest of the experiment though the Lee bounds become increas-ingly wide so that by the end of the experiment we cannot rule out declines (971 pesos or an elasticity of -0.46)or increases (326 pesos or an elasticity of +0.15). In the case of debt, imputing a value of zero for all cancellers isa particularly reasonable approach if policy makers are interested in the overall effect of minimum paymentson debt, not distinguishing between borrowers who remain with the card and accumulate (or decumulate)debt or borrowers who cancel their card and cannot by definition accumulate any more debt with the card.This approach yields qualitatively similar results and the bounds for the implied elasticity tighten on the up-per end so that the new bounds are [−0.44,−0.01]. These results suggest that doubling the minimum paymenthad a statistically significant, modest effect on overall debt.

Figure OA-21: Effect on Debt: Heterogeneity Across Strata and Time

-1500.00-1000.00-500.00

0.00500.00

1000.00

Tre

atm

ent E

ffect

(M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: interest rateDependent variable: debt

-1500.00-1000.00-500.00

0.00500.00

1000.00T

reat

men

t Effe

ct (

MX

N p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: minimum paymentDependent variable: debt

Notes: For each stratum, for each month of the experiment we regress debt on a treatment indicator. Each point (triangle or diamond)corresponds to the coefficient on treatment for that month along with point-wise Lee bounds. For simplicity the comparison grouphere is the (45%, 5%) arm and the comparison group for the interest rate change is the (15%, 5%) arm; the comparison arm for theminimum payment inrease is the (45%, 10%) arm. Each line corresponds to a different stratum. The dark triangles (red or blue)correspond to the “24+ months” stratum and the light diamonds (red or blue) correspond to the “6-11 months” stratum.

Examining heterogeneity in the treatment effects by strata (see Figure OA-21) yields similar results as aboveand we omit the discussion here. To conclude, doubling the minimum payment led to a long-term decrease indebt though the elasticities are probably smaller than those anticipated by policy-makers.

90The late payment fee is 350 pesos for any payment less than the minimum required payment. We summarize the long term effectsof fees in Table OA-19 and note that most of the increases in fees occurred in in the first few months of the experiment. Unfortunately,we do not have information on fees for the first three months of the experiment.

OA - 26

Tabl

eO

A-1

6:Tr

eatm

entE

ffec

tson

Deb

twit

hBa

nkA

Stan

dard

Out

com

eD

eflat

edby

Am

ount

Due

int−

1Se

lect

edSt

rata

(May

/09)

Sep/

07M

ay/0

9M

ay/0

9w

/zer

osSe

p/07

May

/09

Min

.Pay

,6-1

1MFu

llPa

y,24

+MM

in.P

ay,2

4+M

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

r=

15,M

P=

5-2

71.3

06-6

02.9

41-4

19.1

36-0

.016

-0.0

21-6

32.5

27-5

9.69

3-6

84.2

44(8

2.17

9)(6

2.69

8)(4

0.36

7)(0

.006

)(0

.006

)(2

54.2

39)

(80.

647)

(189

.418

)r

=15

,MP

=10

-131

.825

-908

.277

-726

.710

0.00

4-0

.008

-1.3

e+03

-98.

833

-968

.263

(37.

038)

(74.

059)

(59.

372)

(0.0

03)

(0.0

02)

(246

.008

)(7

8.50

7)(1

81.6

10)

r=

25,M

P=

5-1

23.7

28-3

18.2

41-1

99.6

47-0

.002

-0.0

12-1

60.1

46-3

3.82

0-3

26.7

70(9

.845

)(2

6.46

4)(2

6.28

3)(0

.001

)(0

.003

)(2

71.3

26)

(91.

550)

(212

.753

)r

=25

,MP

=10

-76.

255

-860

.327

-704

.486

0.00

8-0

.001

-1.1

e+03

-179

.102

-924

.682

(13.

474)

(60.

496)

(49.

118)

(0.0

03)

(0.0

02)

(251

.472

)(7

1.42

8)(1

81.2

26)

r=

35,M

P=

5-1

4.08

5-3

32.8

18-2

28.2

720.

010

-0.0

11-9

8.67

0-7

0.83

6-4

44.1

17(1

9.27

5)(8

5.63

0)(6

1.02

5)(0

.005

)(0

.005

)(2

69.8

39)

(88.

442)

(196

.150

)r

=35

,MP

=10

-95.

723

-680

.189

-556

.369

0.00

4-0

.009

-1.0

e+03

52.5

46-7

23.5

80(2

3.35

8)(5

7.50

4)(4

4.95

2)(0

.002

)(0

.003

)(2

56.2

32)

(97.

176)

(191

.343

)r

=45

,MP

=10

24.2

43-8

04.0

15-6

99.2

660.

007

-0.0

18-7

50.3

09-2

04.4

48-9

08.6

31(4

6.43

8)(7

8.33

6)(6

3.85

6)(0

.003

)(0

.006

)(2

63.8

20)

(66.

603)

(183

.892

)C

onst

ant(

r=

45,M

P=

5)14

08.7

9421

17.1

3317

35.3

540.

091

0.09

134

32.6

9441

3.44

321

74.6

29(2

18.0

89)

(165

.882

)(1

39.3

43)

(0.0

12)

(0.0

06)

(198

.896

)(5

8.58

0)(1

51.5

27)

Obs

erva

tion

s13

4,38

587

,093

105,

180

120,

189

76,0

827,

820

10,9

489,

839

R-s

quar

ed0.

001

0.00

50.

004

0.00

10.

001

0.00

80.

001

0.00

5Le

eBo

unds

IR[-

397.

281,

-266

.049

][-

1.6e

+03,

-473

.775

][-

851.

598,

-388

.340

][-

0.02

1,-0

.016

][-

0.09

1,-0

.014

][-

1.8e

+03,

-385

.538

][-

379.

885,

-45.

816]

[-1.

8e+0

3,-5

29.8

96]

Lee

Boun

dsM

P[2

1.82

7,10

6.29

3][-

971.

173,

326.

368]

[-76

6.28

4,-0

.595

][0

.005

,0.0

27]

[-0.

023,

0.02

7][-

1.1e

+03,

894.

767]

[-20

5.67

5,-1

35.5

92]

[-1.

1e+0

3,24

4.80

3]ε

Lee

Boun

dsIR

[0.2

8,0.

42]

[0.3

4,1.

12]

[0.3

4,0.

74]

[0.2

6,0.

35]

[0.2

2,1.

50]

[0.1

7,0.

79]

[0.1

7,1.

38]

[0.3

7,1.

23]

εLe

eBo

unds

MP

[0.0

2,0.

08]

[-0.

46,0

.15]

[-0.

44,-

0.00

][0

.06,

0.29

][-

0.25

,0.2

9][-

0.33

,0.2

6][-

0.50

,-0.

33]

[-0.

49,0

.11]

Col

umns

(1)a

nd(4

)are

esti

mat

edfo

rde

bt6

mon

ths

afte

rth

est

arto

fthe

inte

rven

tion

and

the

rem

aind

erar

efo

rm

onth

lypu

rcha

ses

atth

een

dof

the

expe

rim

ent(

26m

onth

s).C

olum

ns(2

)and

(5)p

rese

ntO

LSre

sult

son

the

non-

attr

iter

san

dac

coun

tfo

rat

trit

ion

bypr

esen

ting

Lee

boun

ds(b

otto

m4

row

s).

The

Lee

boun

dsco

mpa

reth

e(r

=15,

MP=

5)an

d(r

=45,

MP=

10)

arm

sag

ains

tth

e(r

=45,

MP=

5)ar

m.

Col

umns

(3)a

nd(6

)red

oth

ean

alys

isby

assi

gnin

ga

zero

toca

rdca

ncel

lers

post

exit

.C

olum

ns(7

),(8)

and

(9)e

stim

ate

the

endl

ine

regr

essi

ons

for

thre

edi

ffer

ents

trat

a–

(a)“

Min

,6-1

1M”

borr

ower

sw

how

ere

wit

hth

eba

nkfo

rle

ssth

ana

year

inJa

nuar

y20

07an

dw

ere

inth

elo

wes

tpa

ymen

tca

tego

ry;(b

)“F

ull,2

4M+”

who

had

been

wit

hth

eba

nkfo

rm

ore

than

2ye

ars

byJa

nuar

y20

07an

dha

dw

ere

inth

ehi

ghes

tpa

ymen

tca

tego

ry;(

c)“M

in,2

4M+”

borr

ower

sw

hoha

dbe

enw

ith

the

bank

for

mor

eth

an2

year

sby

Janu

ary

2007

and

wer

ein

the

low

est

paym

ent

cate

gory

.St

anda

rder

rors

are

show

nin

pare

nthe

ses.

OA - 27

C.4.6 Purchases: Effect of Interest Rates

We begin by examining the effect of the experimental variation in interest rates on purchases in FigureOA-20 and Table OA-17. Figure OA-20 shows monthly treatment effects over the course of the experimentand Table OA-17 presents short- and long-term regression results accounting for attrition. We see in FigureOA-20 that purchases in the 15% arm grew gradually (relative to the 45% arm) over the first year or so of theexperiment. The Lee bounds during the first six months of the intervention are quite tight and the bounds forthe implied short-term elasticity (bottom of Table OA-17 col (1)) are [−0.38,−0.18] indicating modest effectsc.The long-term results, however, are inconclusive. Attrition starts to widen the bounds particularly after thefirst year and by the end of the experiment we cannot rule out increases in monthly purchases of 104 pesos ordeclines of 192 pesos. These imply correspondingly wide bounds on the elasticity ranging from -0.38 to +0.69respectively (bottom of Table OA-17 col (2)). Imputing zeros to purchases for all card cancellers reduces theupper bound, but it remains positive (bottom of Table OA-17 col (3)).

The long-term elasticity bounds are wide but even at the lower bound they are substantially smaller (inabsolute value) than those found in other developing country studies that examine the effect of interest ratechanges on total loan quantity.91 For instance, Karlan and Zinman (2017) compute a two year elasticity of−2.9

of loan quantity with respect to interest rate in an experiment in Mexico with Compartemos. Gross and Souleles(2002) estimate a still high elasticity of −1.3 for credit-card holders in the United States using observationaldata. Dehejia et al. (2012) use plausibly exogenous geographic variation in interest rates to estimate slightlylower but still significant elasticities in the range of (−1.04,−0.73) for micro-credit borrowers in Bangladesh.Our long-term lower-bound is close to the elasticity of −0.32 documented by Karlan and Zinman (2008) forshort-term individual loans in South Africa and also the approximately zero elasticity for auto-loans docu-mented in Attanasio et al. (2008).

91The total quantity of loans demanded might perhaps be thought to correspond to total debt in our context. As we see below,however, debt responds negatively to interest rate reductions in our experiment. Therefore we benchmark our purchase responses tointerest rate changes instead.

OA - 28

Tabl

eO

A-1

7:Tr

eatm

entE

ffec

tson

Mon

thly

Purc

hase

s

Stan

dard

Out

com

eD

eflat

edby

Am

ount

Due

int−

1Se

lect

edSt

rata

(May

/09)

Sep/

07M

ay/0

9M

ay/0

9w

/zer

osSe

p/07

May

/09

Min

.Pay

,6-1

1MFu

llPa

y,24

+MM

in.P

ay,2

4+M

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

r=

15,M

P=

598

.225

63.1

1175

.424

0.01

80.

007

42.4

6212

.398

73.7

87(1

4.88

9)(8

.567

)(5

.671

)(0

.002

)(0

.001

)(4

9.82

1)(1

01.0

33)

(38.

935)

r=

15,M

P=

1016

7.39

625

5.83

921

9.56

70.

033

0.04

120

8.52

6-1

4.71

729

5.63

3(1

6.50

8)(3

2.45

3)(2

4.17

6)(0

.003

)(0

.003

)(5

5.63

1)(1

00.8

48)

(44.

391)

r=

25,M

P=

530

.758

7.48

220

.499

0.00

80.

003

-15.

715

-5.0

499.

415

(11.

336)

(5.5

73)

(3.7

05)

(0.0

01)

(0.0

01)

(50.

215)

(105

.771

)(3

3.37

0)r

=25

,MP

=10

136.

848

177.

373

145.

717

0.02

70.

032

134.

955

-93.

924

208.

505

(13.

409)

(23.

958)

(17.

270)

(0.0

02)

(0.0

04)

(56.

325)

(94.

405)

(37.

990)

r=

35,M

P=

513

.945

17.5

9025

.207

0.00

3-0

.001

-47.

703

63.8

0128

.540

(3.7

39)

(12.

914)

(10.

339)

(0.0

01)

(0.0

02)

(55.

706)

(106

.178

)(3

7.50

6)r

=35

,MP

=10

102.

988

151.

069

124.

285

0.02

10.

024

117.

853

199.

461

151.

997

(9.7

93)

(8.8

19)

(6.2

92)

(0.0

02)

(0.0

03)

(53.

269)

(161

.724

)(3

9.99

8)r

=45

,MP

=10

75.5

3397

.397

64.1

410.

019

0.02

212

5.44

161

.158

86.8

69(9

.333

)(1

1.18

6)(6

.560

)(0

.002

)(0

.001

)(5

5.89

7)(1

18.1

80)

(38.

139)

Con

stan

t(r

=45

,MP

=5)

401.

196

414.

738

339.

949

0.05

80.

060

353.

705

1340

.796

335.

934

(66.

354)

(74.

101)

(61.

634)

(0.0

10)

(0.0

08)

(42.

659)

(72.

779)

(24.

768)

Obs

erva

tion

s13

4,38

587

,093

105,

180

118,

732

78,7

357,

820

10,9

489,

839

R-s

quar

ed0.

002

0.00

40.

003

0.00

60.

010

0.00

60.

001

0.00

9Le

eBo

unds

IR[4

9.02

9,10

0.53

3][-

191.

779,

103.

874]

[-56

.132

,85.

142]

[0.0

18,0

.019

][-

0.03

0,0.

013]

[-15

4.77

2,77

.406

][-

383.

802,

65.4

84]

[-15

7.85

0,11

6.21

8]Le

eBo

unds

MP

[74.

845,

106.

839]

[64.

652,

351.

981]

[51.

012,

231.

490]

[0.0

18,0

.031

][0

.017

,0.0

59]

[85.

467,

401.

779]

[57.

176,

124.

061]

[61.

097,

284.

369]

εLe

eBo

unds

IR[-

0.38

,-0.

18]

[-0.

38,0

.69]

[-0.

38,0

.25]

[-0.

48,-

0.47

][-

0.32

,0.7

6][-

0.33

,0.6

6][-

0.07

,0.4

3][-

0.52

,0.7

0]ε

Lee

Boun

dsM

P[0

.19,

0.27

][0

.16,

0.85

][0

.15,

0.68

][0

.30,

0.53

][0

.29,

0.99

][0

.24,

1.14

][0

.04,

0.09

][0

.18,

0.85

]

Col

umns

(1)

and

(4)

are

esti

mat

edfo

rm

onth

lypu

rcha

ses

6m

onth

saf

ter

the

star

tof

the

inte

rven

tion

and

the

rem

aind

erar

efo

rm

onth

lypa

ymen

tsat

the

end

ofth

eex

peri

men

t(2

6m

onth

s).

Col

umns

(2),(

4)–(

8)dr

opal

lcar

dex

its

and

the

Lee

Boun

dsar

em

ore

info

rmat

ive

than

the

poin

t-es

tim

ates

for

thes

eco

lum

ns.

The

Lee

boun

dsco

mpa

reth

e(r

=15,

MP=

5)an

d(r

=45,

MP=

10)

arm

sag

ains

tth

e(r

=45,

MP=

5)ar

m.

Col

umn

(3)

assi

gns

aze

rofo

ral

lou

tcom

esfo

rca

rdca

ncel

lers

and

the

resu

ltin

gLe

ebo

unds

are

tigh

ter

than

inC

olum

n(2

).C

olum

ns(6

)-(8

)es

tim

ate

endl

ine

regr

essi

ons

for

thre

edi

ffer

ents

trat

a:(a

)“M

inPa

yers

,6-1

1M”

borr

ower

sw

how

ere

wit

hth

eba

nkfo

rm

ore

than

six

mon

ths

butl

ess

than

aye

arin

Janu

ary

2007

and

wer

ein

the

low

estp

aym

ent

cate

gory

;(b)“

Full

Paye

rs,2

4M+”

borr

ower

sw

hoha

dbe

enw

ith

the

bank

for

mor

eth

an2

year

sby

Janu

ary

2007

and

wer

ein

the

high

estp

aym

entc

ateg

ory;

(c)“

Min

Paye

rs,2

4M+”

borr

ower

sw

hoha

dbe

enw

ith

the

bank

for

mor

eth

an2

year

sby

Janu

ary

2007

and

wer

ein

the

low

estp

aym

entc

ateg

ory

atba

selin

e.St

anda

rder

rors

are

show

nin

pare

nthe

ses.

OA - 29

We also examined treatment effects after normalizing purchases by the amount due each month and ob-tained relatively sharp results in the short-run but the effect is even weaker in the long-run. At the six-monthmark, the bounds on fraction purchased is fairly tight around .018 (relative to a comparison group fractionof .06) while in the long run the bounds include zero and and are consistent with both small increases andsignificant declines in purchases.

In summary, the effect of interest rate reductions on purchases appears to be relatively small relative to theprevious literature.

Figure OA-22: Effect on Purchases: Heterogeneity Across Strata and Time

-200.00

0.00

200.00

400.00

600.00

Tre

atm

ent E

ffect

(M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: interest rateDependent variable: purchases

-200.00

0.00

200.00

400.00

600.00

Tre

atm

ent E

ffect

(M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: minimum paymentDependent variable: purchases

For each stratum, for each month in the experiment we regress purchases on a treatment dummy. Each dot corresponds to thecoefficient on the treatment dummy for that month along with point-wise Lee bounds. For simplicity the comparison group here isthe (45%, 5%) ground and the treatment group for the interest rate change is the (15%, 5%) ground and the (45%, 10%) group for theminimum payment intervention. Each line corresponds to a different stratum. The dark triangles correspond to the “24+ months”stratum and the light diamonds correspond to the “6-11 months” stratum.

C.4.7 Purchases: Effects of Minimum Payments

Doubling the minimum payment led to an increase in monthly purchases. Figure OA-20 shows that pur-chases increase gradually over the first six months of the experiment after which there appears to be no sys-tematic increase. The short-term effect of the raise in payment requirements increased purchases by about75 pesos per month, with the Lee bounds being relatively tight at[75, 107], and the corresponding elasticitybounds are similarly tight at [.19, .27] suggesting a modest positive effect.

This point estimate remains more or less stable over the remainder of the experiment even though attritionincreases and the bounds start to widen. The lower Lee bound at the end of the experiment is 65 pesos andthe upper Lee bound is 352 pesos – implying lower and upper bounds on the elasticities of 0.16 and 0.85

respectively. We obtain broadly similar results if we impute zeros to all cancellations with the only significantchange being that the upper Lee bound reduces to 0.68.

The increase in purchases is somewhat unexpected. In principle, it could arise from higher payments easingborrowers credit lines. However, this is not the case since the point estimates and bounds are very similar whenwe restrict attention to borrowers who are at less than 50% of their credit limit.92 Alternatively, since higherminimum payments imply, ceteris paribus, a decrease in debt, the increase in purchases may reflect changes inborrower behavior as a result of reduced debt. This argument implies that the effect of minimum payments onpurchases should be higher for borrowers who see larger reductions in debt. We explore this implication by

92Results available upon request.

OA - 30

examining the changes in purchases across the various interest rate arms keeping the required payment fixedat 10%.

Finally, as expected, the “Full,24M+” stratum is largely unaffected by the minimum payment increasethroughout the intervention while the effect is stronger for the “Min,12M–” stratum and the bounds for theimplied elasticities are consistent with both modest (0.24) and substantive (1.14) effects. Finally, we also nor-malized monthly purchases by expressing purchases as a fraction of amount due (cols (4) and (5) of TableOA-17) and the results were similar to the ones described above so we omit a discussion. To summarize,monthly purchases rose modestly but persistently and (statistically) significantly for borrowers who were inthe higher minimum payment arm.

C.4.8 Payments: Effect of Interest Rates

Figure OA-20 presents the Lee bounds along with the point estimates from equation (8) for each month inthe experiment. We see that there is a gradual decline in monthly payments during the first six months andthe bounds at the six-month mark are [−103,−24] pesos with implied elasticity bounds of [.06, .24] suggestingrelatively modest declines in payments.

The upper bound remains relatively stable over the remainder of experiment but the lower bound beginsto widen in the last months of 2007 and by the end of the experiment the data is consistent with both small(17 pesos) and substantial (267 pesos) declines in monthly payments. These final bounds imply elasticitiesof monthly payments with respect to interest rates ranging from 0.04 to 0.64 respectively. Estimating thelong-term effects after setting monthly payments to zero for cancelled cards tightens the upper bound for theelasticity so that the new bounds are [0.04, 0.39].

The evidence then suggests that declines in interest rates led to modest, yet discernible, declines in monthlypayments. The fact that monthly payments actually decreased when interest rates fell suggests that the pri-mary channel through which the interest rate effects function is via reducing the rate at which outstandingdebt is compounded.

We also explored treatment effects on payments by examining two other outcome variables – (a) a binaryvariable equal to 1 if the borrower paid at least 5% of the amount outstanding each month and (b) the paymentexpressed as a fraction of the amount outstanding each month. The results for both are consistent with theprevious results and we omit the discussion.

OA - 31

Figure OA-23: Effect on Payments: Heterogeneity Across Strata and Time

-400.00

-200.00

0.00

200.00

400.00

600.00

Tre

atm

ent E

ffect

(M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: interest rateDependent variable: payments

-400.00

-200.00

0.00

200.00

400.00

600.00

Tre

atm

ent E

ffect

(M

XN

pes

os)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

6-11 m 24+ m

Treatment: minimum paymentDependent variable: payments

Notes: For each stratum, for each month in the experiment we regress payments in that month on a treatment dummy. Each dotcorresponds to the coefficient on the treatment dummy for that month along with point-wise Lee bounds. For simplicity the com-parison group here is the (45%, 5%) control group and the treatment group for the interest rate change is the (15%, 5%) group andthe (45%, 10%) group for the minimum payment intervention. Each line corresponds to a different stratum. The dark red trianglescorrespond to the “24+ months” stratum and the light red diamonds correspond to the “6-11 months” stratum.

C.4.9 Payments: Effect of Minimum Payment

It is reasonable to expect that the most direct effect of the minimum payment intervention would be onmonthly payments. Figure OA-20 documents a sharp increase in monthly payments in the treatment group inthe third month of the experiment93 (May 2007) and after a small increase in the next month there is a steadydecline over the remainder of the experiment. The six month treatments effects are precisely estimated andthe Lee Bounds for the implied elasticity are very tight at [.24, .29] suggesting small, though robust, effects ofthe increase in required payments. The bounds then begin to widen considerably starting in the last monthsof 2007 and remain relatively wide throughout the remainder of the experiment. By the end of the experimentattrition widens the bounds considerably and the bounds for the implied elasticity, while still positive, rangefrom 0.01 to 0.48. Imputing zero values to card cancellations provides qualitatively similar results with theupper bound tightened to 0.37. These bounds indicate that the implied effects, even at the upper bound, arerelatively small in substantive terms. We also consider the effect of the treatment on monthly payments mea-sured as a fraction of the amount due in each month. The results suggest are broadly similar to the previousanalysis with the short term bounds on the elasticity being [0.24, 0.35] and the long-term bounds are some-what wider at [.16, .58]. The patterns of heterogeneity in treatment effects are as expected with no effects onthe “Full, 24M+” stratum and larger effects for the other strata particularly the “Min,12M–” stratum thougheven in that case the effects are not particularly large.

93Initial borrower inattention is a plausible explanation for the lack of response in the first two months. In particular, we see a corre-sponding increase in delinquencies in the first two months of the intervention followed by a decline. Further, we see a correspondingincrease in late fees as well in the first two months of the intervention.

OA - 32

Tabl

eO

A-1

8:Tr

eatm

entE

ffec

tson

Mon

thly

Paym

ents

Stan

dard

depe

nden

tvar

iabl

eD

eflat

edby

amou

ntdu

eint−

1Se

lect

edst

rata

inM

ay/0

9

Sep/

07M

ay/0

9M

ay/0

9w

/zer

osSe

p/07

May

/09

Min

.Pay

,6-1

1MFu

llPa

y,24

+MM

in.P

ay,2

4+M

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

r=

15,M

P=

5-2

7.31

9-6

5.23

5-2

5.59

3-0

.003

-0.0

12-1

3.83

1-1

01.7

47-6

8.75

4(1

1.69

6)(8

.418

)(7

.922

)(0

.001

)(0

.002

)(4

6.61

1)(1

01.9

12)

(36.

571)

r=

15,M

P=

1012

8.59

710

7.57

798

.989

0.03

10.

028

124.

880

-13.

804

134.

640

(16.

417)

(20.

897)

(15.

594)

(0.0

03)

(0.0

04)

(48.

917)

(109

.685

)(4

3.85

0)r

=25

,MP

=5

-23.

121

-62.

865

-32.

318

-0.0

02-0

.007

-23.

186

-102

.743

-65.

769

(10.

161)

(8.3

19)

(8.1

32)

(0.0

02)

(0.0

00)

(48.

735)

(110

.701

)(3

6.16

0)r

=25

,MP

=10

133.

639

92.1

0075

.892

0.03

00.

029

99.0

53-7

4.69

410

0.19

9(9

.086

)(9

.075

)(6

.674

)(0

.003

)(0

.003

)(4

9.67

2)(1

02.7

18)

(38.

464)

r=

35,M

P=

523

.434

10.4

9424

.524

0.00

1-0

.002

-32.

696

19.6

2427

.748

(5.5

26)

(12.

718)

(13.

363)

(0.0

01)

(0.0

01)

(43.

325)

(111

.886

)(4

3.19

3)r

=35

,MP

=10

160.

415

99.3

7982

.046

0.03

40.

026

144.

575

95.1

7110

8.13

3(1

9.47

2)(8

.184

)(8

.585

)(0

.004

)(0

.002

)(4

8.35

5)(1

61.4

54)

(47.

500)

r=

45,M

P=

1015

4.53

958

.212

26.7

030.

029

0.02

616

2.78

4-2

3.41

332

.274

(12.

554)

(20.

692)

(15.

828)

(0.0

01)

(0.0

01)

(57.

049)

(108

.380

)(3

8.97

0)C

onst

ant(

r=

45,M

P=

5)63

7.64

362

7.48

651

4.33

30.

115

0.10

553

0.36

914

02.3

7457

5.20

4(4

5.85

7)(5

3.95

0)(4

5.42

7)(0

.016

)(0

.010

)(3

3.24

8)(8

6.45

5)(2

9.02

1)

Obs

erva

tion

s13

4,38

587

,093

105,

180

125,

152

79,6

127,

820

10,9

489,

839

R-s

quar

ed0.

003

0.00

30.

002

0.00

80.

013

0.00

50.

000

0.00

5Le

eBo

unds

IR[-

102.

895,

-24.

498]

[-26

6.50

2,-1

7.27

3][-

134.

228,

-14.

158]

[-0.

005,

-0.0

02]

[-0.

043,

-0.0

03]

[-19

6.58

3,31

.730

][-

400.

173,

-50.

724]

[-24

7.65

6,-1

6.30

5]Le

eBo

unds

MP

[153

.445

,184

.136

][8

.669

,301

.360

][6

.840

,192

.554

][0

.028

,0.0

40]

[0.0

17,0

.061

][1

02.8

45,3

75.1

04]

[-27

.578

,84.

002]

[-11

.854

,236

.821

]ε

Lee

Boun

dsIR

[0.0

6,0.

24]

[0.0

4,0.

64]

[0.0

4,0.

39]

[0.0

3,0.

07]

[0.0

4,0.

62]

[-0.

09,0

.56]

[0.0

5,0.

43]

[0.0

4,0.

65]

εLe

eBo

unds

MP

[0.2

4,0.

29]

[0.0

1,0.

48]

[0.0

1,0.

37]

[0.2

4,0.

35]

[0.1

6,0.

58]

[0.1

9,0.

71]

[-0.

02,0

.06]

[-0.

02,0

.41]

Col

umns

(1)a

nd(4

)are

esti

mat

edfo

rm

onth

lypa

ymen

ts6

mon

ths

afte

rth

est

arto

fthe

inte

rven

tion

and

the

rem

aind

erar

efo

rm

onth

lypa

ymen

tsat

the

end

ofth

eex

peri

men

t(26

mon

ths)

.Col

umns

(2),(

5)–(

8)dr

opal

lcar

dex

its

and

the

Lee

Boun

dsar

em

ore

info

rmat

ive

than

the

poin

t-es

tim

ates

for

thes

eco

lum

ns.

The

Lee

boun

dsco

mpa

reth

e(r

=15,

MP=

5)an

d(r

=45,

MP=

10)

arm

sag

ains

tthe

(r=4

5,M

P=5)

arm

.C

olum

n(3

)as

sign

sa

zero

for

all

outc

omes

for

card

canc

elle

rsan

dth

ere

sult

ing

Lee

boun

dsar

eti

ghte

rth

anin

Col

umn

(2).

Col

umns

(7)-

(9)

esti

mat

een

dlin

ere

gres

sion

sfo

rth

ree

diff

eren

tstr

ata:

(a)“

Min

Paye

rs,6

-11M

”bo

rrow

ers

who

wer

ew

ith

the

bank

for

mor

eth

ansi

xm

onth

sbu

tles

sth

ana

year

inJa

nuar

y20

07an

dw

ere

inth

elo

wes

tpay

men

tcat

egor

y;(b

)“Fu

llPa

yers

,24M

+”bo

rrow

ers

who

had

been

wit

hth

eba

nkfo

rm

ore

than

2ye

ars

byJa

nuar

y20

07an

dw

ere

inth

ehi

ghes

tpay

men

tcat

egor

y;(c

)“M

inPa

yers

,24M

+”bo

rrow

ers

who

had

been

wit

hth

eba

nkfo

rm

ore

than

2ye

ars

byJa

nuar

y20

07an

dw

ere

inth

elo

wes

tpay

men

tcat

egor

yat

base

line.

Stan

dard

erro

rsar

esh

own

inpa

rent

hese

s.

OA - 33

Finally, we also examine two other outcome variables – (a) a binary variable equal to 1 if the borrowerpaid at least 5% of the amount outstanding each month and (b) the payment expressed as a fraction of theamount outstanding each month. The results for both are consistent with the previous results and we omit thediscussion.

Our overall conclusion from the results above is that a doubling of the minimum payment had a long-termpositive, albeit modest, effect on monthly payments.

C.4.10 Effect on Fees

The effect of the interventions on card fees are summarized in Table OA-19 and Figure OA-24. Monthlyfees averages about 28 pesos in the base group and this amount remained more or less unchanged through the26 month study period (fees were about 4% of monthly payments).94

The interest rate decline has a modest negative long-term effect on average fees although the bounds arequite wide ranging from +0.15 to +1.22. In contrast, the effect of the minimum payment increase is only veryimprecisely estimated with the Lee bounds covering zero and ranging from −0.19 to +0.47.

Table OA-19: Treatment Effects on Fees

Standard dependent variable Selected strata in May/09

Sep/07 May/09 Min.Pay, 6-11M Full Pay,24+M Min.Pay,24+M(1) (2) (3) (4) (5)

r = 15, MP = 5 -2.68 -4.58 -1.33 -1.01 -6.62(1.42) (1.52) (3.50) (1.41) (2.65)

r = 15, MP = 10 4.12 -4.12 -7.71 -0.20 -4.71(0.73) (0.63) (3.45) (1.46) (2.76)

r = 25, MP = 5 -2.39 -4.19 -1.80 -0.94 -5.50(0.99) (1.00) (3.51) (1.44) (2.68)

r = 25, MP = 10 4.68 -3.93 -4.18 -2.21 -4.30(0.75) (0.32) (3.53) (1.35) (2.79)

r = 35, MP = 5 -0.29 -1.60 0.65 -1.70 -3.45(0.53) (1.45) (3.56) (1.38) (2.76)

r = 35, MP = 10 4.25 -1.58 -3.14 2.36 -1.65(1.18) (0.46) (3.55) (1.66) (2.89)

r = 45, MP = 10 6.22 -2.74 -7.58 -0.41 -2.76(1.29) (0.46) (3.49) (1.47) (2.90)

Constant (r = 45, MP = 5) 27.96 26.44 37.04 7.22 27.14(0.71) (0.63) (2.54) (1.04) (2.03)

Observations 134,306 87,027 7,804 10,948 9,828R-squared 0.002 0.001 0.001 0.001 0.001Lee bounds r [ -3.54, -2.59] [-21.45, -2.73] [-17.72, 1.85] [ -7.22, -0.77] [-25.95, -4.50]Lee bounds MP [ 6.15, 6.33] [ -5.02, 12.35] [-11.71, 12.98] [ -0.43, 0.22] [ -4.84, 12.06]Lee bounds ε r [ 0.14, 0.19] [ 0.15, 1.22] [ -0.07, 0.72] [ 0.16, 1.50] [ 0.25, 1.43]Lee bounds ε MP [ 0.21, 0.21] [ -0.19, 0.47] [ -0.32, 0.35] [ -0.06, 0.03] [ -0.18, 0.44]

Columns (1) is estimated for monthly fees 6 months after the start of the intervention and the remainder are for monthly fees atthe end of the experiment (27 months). Columns (2)-(5) drop all card exits (so the Lee Bounds are most relevant). The Lee boundscompare (r=15, MP=5) and (r=45,MP=10) arms against the (r=45, MP=5) arm. Columns (3)-(5) estimate the endline regressionsfor three different strata – (a) “Min Payers, 6-11M” borrowers who were with the bank for more than six months but less than ayear in January 2007 and were in the lowest payment category ;(b) “Full Payers,24M+” borrowers who had been with the bankfor more than 2 years by January 2007 and were in the highest payment category; (c) “Min Payers,24M+” borrowers who hadbeen with the bank for more than 2 years by January 2007 and were in the lowest payment category at baseline.

94Unfortunately, we do not have information on fees for the first three months of the experiment.

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Figure OA-24: Effect on Fees: Heterogeneity Across Strata and Time

-20.00-10.00

0.0010.0020.00

Trea

tmen

t Effe

ct (M

XN p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Min. payers w/ 6-11 m Full payers w/ 24+ m

Treatment: interest rateDependent variable: fees incurred

-20.00-10.00

0.0010.0020.00

Trea

tmen

t Effe

ct (M

XN p

esos

)

Mar/07 Sep/07 Mar/08 Sep/08 Mar/09

Min. payers w/ 6-11 m Full payers w/ 24+ m

Treatment: minimum paymentDependent variable: fees incurred

For each stratum, for each month in the experiment we regress fees on a treatment dummy. Each dot corresponds to the coefficient onthe treatment dummy for that month along with point-wise Lee bounds. For simplicity the comparison group here is the (45%, 5%)ground and the treatment group for the interest rate change is the (15%, 5%) ground and the (45%, 10%) group for the minimumpayment intervention. Each line corresponds to a different stratum. The dark triangles correspond to the “24+ months” strata and thelight diamonds correspond to the “6-11 months” strata.

C.4.11 Effect on other loans

Table OA-20: Treatment Effects on Other Cards: Default, Cancellations and New LoansExisting loans by March 2007, Outcomes measured in June 2009.

Default Cancellations New card

Any Same Other Any Same Other Any Same OtherBank Bank Bank Bank Bank Bank Bank Bank Bank

(1) (2) (3) (4) (5) (6) (7) (8) (9)

r = 15, MP = 5 0.004 0.007 -0.001 0.011 0.002 0.010 0.011 0.008 0.012(0.003) (0.003) (0.002) (0.008) (0.001) (0.007) (0.006) (0.002) (0.007)

r = 15, MP = 10 -0.009 -0.012 -0.002 0.016 0.005 0.011 0.011 0.009 0.010(0.003) (0.005) (0.003) (0.009) (0.002) (0.007) (0.007) (0.003) (0.006)

r = 25, MP = 5 0.001 -0.002 0.002 0.004 0.001 0.002 0.003 0.001 0.003(0.004) (0.001) (0.003) (0.004) (0.002) (0.003) (0.005) (0.003) (0.005)

r = 25, MP = 10 -0.006 -0.002 -0.006 0.003 0.003 -0.000 0.003 0.001 0.005(0.005) (0.003) (0.004) (0.005) (0.003) (0.004) (0.005) (0.001) (0.004)

r = 35, MP = 5 -0.003 0.000 -0.002 0.002 0.000 0.002 0.006 0.001 0.005(0.002) (0.003) (0.002) (0.003) (0.001) (0.002) (0.004) (0.001) (0.005)

r = 35, MP = 10 -0.001 0.001 -0.004 0.006 0.000 0.006 -0.005 -0.001 -0.002(0.007) (0.004) (0.008) (0.004) (0.001) (0.003) (0.002) (0.003) (0.001)

r = 45, MP = 10 -0.026 -0.016 -0.017 0.007 -0.000 0.006 -0.017 -0.008 -0.008(0.010) (0.007) (0.008) (0.004) (0.001) (0.004) (0.007) (0.005) (0.003)

Constant (r = 45, MP = 5) 0.498 0.222 0.428 0.096 0.018 0.082 0.424 0.137 0.366(0.003) (0.003) (0.003) (0.005) (0.001) (0.003) (0.002) (0.001) (0.003)

Observations 143,916 143,916 143,916 143,916 143,916 143,916 143,916 143,916 143,916R-squared 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Notes: All regressions include strata dummies and use sample weights. This is the analogous table to Table 3 but restricted exclusivelyto credit cards. The dependent variable for Columns (1) to (3) is default (bank-initiated revocations). The dependent variable forColumns (4) to (6) are (client-initiated) cancellations. The dependent variable for Columns (7) to (9) are new loan originations. Allcolumns exclude the experimental card. Columns (1), (4) and (7) refer to loans issued by any bank. Columns (2), (5) and (8) refer toloans issued by the same bank as the experimental card (i.e. Bank A). Columns (3), (6) and (9) refer to loans issued by any bank exceptfor Bank A. All dependent variables restrict to loans that were issued on or before by March 2007 that remained active by March 2007.All outcomes are measured in June 2009, one month after the experiment ended.

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C.5 Comparison of min. payment across treatment arms 3 years after the experiment ended

Figure OA-25: Payment as a fraction of debt 3 years after the experiment

(a) Jun/12 - treatment arms with mp = 5%

0.15

0.01

0.06

0.28

0.11

0.060.05

0.040.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

0.11

0.1

.2.3

.4Fr

actio

n of

car

dhol

ders

0 .1 .2 .3 .4 .5Payment as proportion of amount due

(b) Jun/12 - treatment arms with mp = 10%

0.14

0.01

0.05

0.29

0.11

0.060.05

0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00

0.11

0.1

.2.3

.4Fr

actio

n of

car

dhol

ders

0 .1 .2 .3 .4 .5Payment as proportion of amount due

Notes: We plot monthly payment divided by the amount due. In Panels (a) and (b) we examine the ratio of monthly payments in June2012 to the amount due in the May 2012 statement. We examine separately cardholders by the minimum payment group (poolingacross interest rates groups) during the experimental period (Mar/07-May/09). We right-censor all figures at .5, so the rightmost binfor each panel includes those whose payment ratio is 0.5 or higher. The leftmost bin starts at 0, and all bins have a width of 0.25. Thenumber above each bin represents the fraction of cardholders in the given bin. The variable in the x-axis is only an approximation tothe minimum payment since the minimum payment may include some fees or discounts that we do not observe.

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Appendix D. Habit formation

Table OA-21: Habit formation regressions

No controls Months with CC strata Months + Current TermsFirst stage Second stage First stage Second stage First stage Second stage

(1) (2) (3) (4) (5) (6)

r = 15 618 616 295(150) (150) (110)

MP = 10 5.1 7.3 4.7 7.5 44 3.8(138) (28) (138) (28) (86) (28)

Min. payer 1383 -475 1383 -478 224 -433(158) (59) (157) (59) (108) (34)

MP = 10 ×Min. payer -159 32 -160 32 -26 28(233) (40) (233) (40) (157) (39)

Amount due 0.097 0.097 0.14(0.035) (0.036) (0.075)

Strata FE no no yes yes yes yesCurrent card terms no no no no yes yesDependent variable mean 6680 748 6680 748 6680 748Observations 33,206 33,206 33,206 33,206 33,206 33,206R-squared 0.0084 0.1683 0.0118 0.1689 0.5109 0.1780

Notes: Robust standard errors are shown in parenthesis. The sample is those cards that (i) participated in the experiment (ii) remainedopened by 2010, and (iii) were assigned to either the highest or lowest interest rate groups (eg. [r = 15, MP = 5], [r = 15, MP = 10], [r= 45, MP = 5], and [r = 15, MP = 10]). Each column represents a different regression. Columns (2), (4) and (6) have as a dependentvariable the amount paid on June 2010, as a function of the minimum payment that was assigned during the experiment and debt.Since debt can be endogenous, we instrument for debt using the interest rate group cardholders were assigned to. We also allow fora differential treatment effect for those in the "minimum-payment" strata. The dependent variable of Columns (1), (3) and (5) is theamount due on June 2010. Columns (1) and (2) show the regression equations without additional controls. Columns (3) and (4) addthe months with credit cards strata dummies. Columns (5) and (6) add both the months with credit cards strata dummies as well ascurrent contract terms, namely the interest rate and the required minimum payment in pesos in June 2010.

Appendix E. Comparisons

Table OA-22: Comparisons with the Literature

Paper Outcome Table (page) Point Estimate Elasticity

Karlan and Zinman (2007) Account in Collection 3 (p.40) -1.6 +0.27Karlan and Zinman (2017) Delinquency 5 (p.42) -0.0196 +1.80Adams et al. (2009) Default Hazard 4 (p.28) 1.022 +2.2Keys and Wang (2016) Delinquency p.4 .01 +0.20d’Astous and Shore (2017) Default p.3 .04 +0.06

Notes: We use the working paper version of Karlan and Zinman (2009). Table 3 cols (4) and (5) for the “repayment burden effect.” Thetable reports a decline from 13.9 to 12.3 in the percentage of accounts in collection status over a four month period. The differencebetween the high and the low interest rate was on average 350 basis points. We use the high risk category upper bound for theinterest rate of 11.75 percent as the base rate and convert the monthly interest rates to APR to facilitate comparisons (the calculationis (−1.6/13.9)(279/− 120) = .27). For Karlan and Zinman (2017) we use the results from Table 5 (col (4), Panel B) that delinquenciesdecline by 1.96 percentage points off of a control baseline of 10.5%. Low rate regions faced APRs of 80% while high rate regions facedAPRs of 90%. The implied elasticity is (−2/10)/(80− 90/90) = 1.8. Adams et al. (2009) estimate a hazard model and the hazard ratesuggests that a one percent increase in the APR leads to a 2.2 percent increase in the hazard rate of default. Keys and Wang (2016) andd’Astous and Shore (2017) study changes in minimum payments while the remaining papers examine interest rate variation.

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Appendix F. Mechanisms

F.1 Consequences of default

Figure OA-26: Comparison formal and informal loan market in Mexico

(a) Interest rate

0.2

.4.6

.81

Fra

ctio

n

0 20 40 60 80 100Annual Interest Rate

Formal loans Informal loans

(b) Loan duration

0.2

.4.6

.81

Fra

ctio

n

0 1 2 3Years to Pay Loan

Formal Loans Informal loans

(c) Loan amount

0.2

.4.6

.81

Fra

ctio

n

0 5000 10000 15000 20000 25000Loan Amount

Formal LoansInformal loans

Notes: The above figures compare the formal and informal credit market in Mexico using the annual interest rate (a), the loan tenurein years (b) and the loan amount in pesos (c). This data comes from ENNVIH survey reported by the INEGI on years 2002, 2005, and2009. The lines represent the cumulative distribution of the three variables; divided between formal and informal.

Table OA-23: Access to loans after the first delinquency

any new loan with any bank any new loan with other banks any new loan with bank Ab/se b/se b/se(1) (2) (3)

after first delinquency -0.02 -0.02 -0.01(0.00) (0.00) (0.00)

mean dep. var before default 0.070 0.057 0.015Observations 354,255 354,255 354,255R-squared 0.023 0.016 0.012

Notes: This table focuses on the sample of borrowers on the experimental sub-sample for whom the study card was the first formalsector loan product and who had been with Bank A between 6 to 11 months at the start of the experiment. We observe 55 months ofdata, from March/07 to Sept/11. We further restrict the sample to borrowers who defaulted in this period. This leaves us with 6,441borrowers. For each of those borrowers we locate the first month they were delinquent (i.e. 30 days past due) on the experimentalcard, and create an indicator for any time period after this first delinquency I(After 1st Del for i)it. We estimate by OLS the regressionyit = αi + γt + β I(After 1st Del for i)it + εit, where yit is an indicator for borrower i getting a new loan (any kind of loan) in periodt with any bank (column 1), non-Bank A (column 2), or Bank A (column 3). The table reports estimated β’s, as well as the mean ofthe dependent variable in the periods before default; β’s estimates the within borrower difference of the likelihood of get new loans inperiods after delinquency compared to the likelihood of getting new loans before being delinquent, for the same borrower.

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Appendix G. Comparison with Compartamos and Azteca

Figure OA-27: Operational Costs (relative to Assets)

0%10

%20

%30

%40

%Av

erag

e

MFIs Compartamos Banco Azteca Bank A

Bank

Operational Cost

Notes: The cost ratio is defined as the ratio of administrative and promotion spending to total assets. Data is taken from the MexicanBanking Comission (CNBV) at https://portafoliodeinformacion.cnbv.gob.mx/bm1/Paginas/infosituacion.aspx (under 040-5Z-R6, indicadores financieros). We average annual figures from 2007-2009 to be consistent with the study period.

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